S.O.N.G/c-gaborator
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/.idea
/build
/cmake-build-debug

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[submodule "lib/pffft"]
path = lib/pffft
url = https://github.com/marton78/pffft.git

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cmake_minimum_required(VERSION 3.16)
project(c_gaborator)
set(CMAKE_CXX_STANDARD 11)
set(CMAKE_POSITION_INDEPENDENT_CODE ON)
if(NOT CMAKE_BUILD_TYPE)
set(CMAKE_BUILD_TYPE Release)
endif()
set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -ggdb -O0")
set(CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE} -O3")
add_definitions(-DGABORATOR_USE_PFFFT)
include_directories(lib/gaborator)
include_directories(lib/pffft)
find_library(libpffft NAMES pffft PATHS ${PROJECT_SOURCE_DIR}/lib/pffft/install/lib NO_DEFAULT_PATH REQUIRED)
add_library(cgaborator cgaborator.cpp)
target_link_options(cgaborator PRIVATE -static-libgcc -static-libstdc++ "LINKER:--as-needed")
target_link_libraries(cgaborator "${libpffft}")

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LICENSE Normal file
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c-gaborator is Copyright (C) 2022 WeebDataHoarder.
License to distribute and modify the code is hereby granted under the
terms of the GNU Affero General Public License, version 3 (henceforth,
the AGPLv3), but not under other versions of the AGPL. See below for
the full text of the AGPLv3.
---
The Gaborator library is Copyright (C) 1992-2019 Andreas Gustafsson.
License to distribute and modify the code is hereby granted under the
terms of the GNU Affero General Public License, version 3 (henceforth,
the AGPLv3), but not under other versions of the AGPL. See below for
the full text of the AGPLv3.
If the terms of the AGPLv3 are not acceptable to you, commercial
licensing under different terms is possible. Please contact
info@gaborator.com for more information.
---
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#!/bin/bash
set -ex
pushd "${0%/*}"
pushd lib
pushd pffft
if [[ -d "build" ]]; then
rm -r build
fi
if [[ -d "install" ]]; then
rm -r install
fi
mkdir build
mkdir install
pushd build
cmake .. -DUSE_TYPE_FLOAT=OFF -DUSE_TYPE_DOUBLE=ON -DCMAKE_INSTALL_PREFIX="$(pwd)/../install"
make -j$(nproc)
make install

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#include <iostream>
extern "C" {
#include "cgaborator.h"
}
#include "gaborator/gaborator.h"
#include <unordered_map>
#include <math.h>
#include <mutex>
const int C_ARRAY_SIZE = 300000 * 2;
struct GaboratorState {
gaborator::parameters* paramsRef;
gaborator::analyzer<float>* analyzerRef;
gaborator::coefs<float>* coefsRef;
int64_t t_in;
int min_band;
int sample_rate;
int64_t anal_support;
std::mutex stateMutex;
float cArray[C_ARRAY_SIZE];
};
void* gaborator_initialize(int blockSize, double sampleRate, int bandsPerOctave, double minimumFrequency, double maximumFrequency, double referenceFrequency){
auto state = new GaboratorState();
std::unique_lock<std::mutex> lck (state->stateMutex);
state->paramsRef = new gaborator::parameters(bandsPerOctave, minimumFrequency / sampleRate, referenceFrequency / sampleRate, 1.0, 1e-5);
state->analyzerRef = new gaborator::analyzer<float>(*(state->paramsRef));
state->coefsRef = new gaborator::coefs<float>(*(state->analyzerRef));
//converts frequency (ff_max) in hertz to the number of bands above the min frequency
//the ceil is used to end up at a full band
int interesting_bands = ceil(bandsPerOctave * log(maximumFrequency/sampleRate)/log(2.0f));
//since bands are ordered from high to low we are only interested in lower bands:
//fs/2.0 is the nyquist frequency
int total_bands = ceil(bandsPerOctave * log(sampleRate/2.0/minimumFrequency)/log(2.0f));
state->anal_support = (int64_t) ceil(state->analyzerRef->analysis_support());
state->min_band = total_bands - interesting_bands;
state->sample_rate = (int) sampleRate;
state->t_in = 0;
assert(state->t_in == 0);
return state;
}
long gaborator_get_anal_support(void* ptr) {
return reinterpret_cast<GaboratorState*>(ptr)->anal_support;
}
void gaborator_analyze(void* ptr, float* audio_block, int audio_block_length) {
auto state = reinterpret_cast<GaboratorState*>(ptr);
std::vector<float> buf(audio_block,audio_block + audio_block_length);
int output_index = 0;
state->analyzerRef->analyze(buf.data(), state->t_in, state->t_in + audio_block_length, *(state->coefsRef));
int64_t st0 = state->t_in - state->anal_support;
int64_t st1 = state->t_in - state->anal_support + audio_block_length;
apply(
*state->analyzerRef,
*state->coefsRef,
[&](std::complex<float> coef, int band, int64_t audioSampleIndex ) {
//ignores everything above the max_band
if(band >= state->min_band){
//printf("%f %d %ld\n",std::abs(coef),band,audioSampleIndex);
state->cArray[output_index++] = band;
state->cArray[output_index++] = audioSampleIndex;
state->cArray[output_index++] = std::abs(coef);
//printf("output_index: %d\n", output_index++);
//output_index++;
}
},st0,
st1);
state->t_in += (int64_t) audio_block_length;
int64_t t_out = state->t_in - state->anal_support;
forget_before(*state->analyzerRef, *state->coefsRef, t_out - audio_block_length);
}
float* gaborator_get_array(void* ptr) {
auto state = reinterpret_cast<GaboratorState*>(ptr);
return state->cArray;
}
int gaborator_get_array_length(void* ptr) {
auto state = reinterpret_cast<GaboratorState*>(ptr);
return sizeof(state->cArray) / sizeof(state->cArray[0]);
}
int gaborator_bandcenters_array_length(void* ptr) {
auto state = reinterpret_cast<GaboratorState*>(ptr);
int max_band = state->analyzerRef->bandpass_bands_end();
return max_band+1;
}
void gaborator_bandcenters(void* ptr, float* band_centers) {
auto state = reinterpret_cast<GaboratorState*>(ptr);
int max_band = state->analyzerRef->bandpass_bands_end();
//band_centers = new float[max_band+1]; //TODO
for(int i = 0 ; i < max_band ; i++){
if(i<state->min_band){
band_centers[i]=-1;
}else{
band_centers[i]=state->analyzerRef->band_ff(i) * state->sample_rate;
}
}
}
void gaborator_release(void* ptr) {
auto state = reinterpret_cast<GaboratorState*>(ptr);
std::unique_lock<std::mutex> lck (state->stateMutex);
//cleanup memory
delete state->analyzerRef;
delete state->coefsRef;
delete state->paramsRef;
delete state;
}

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cgaborator.h Normal file
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void* gaborator_initialize(int blockSize, double sampleRate, int bandsPerOctave, double minimumFrequency, double maximumFrequency, double referenceFrequency);
long gaborator_get_anal_support(void* ptr);
void gaborator_analyze(void* ptr, float* audio_block, int audio_block_length);
float* gaborator_get_array(void* ptr);
int gaborator_get_array_length(void* ptr);
int gaborator_bandcenters_array_length(void* ptr);
void gaborator_bandcenters(void* ptr, float* band_centers);
void gaborator_release(void* ptr);

99
lib/gaborator/CHANGES Normal file
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1.7
Miscellaneous bug fixes.
Support lower numbers of bands per octave, down to 4.
Further improve the performance of analyzing short signal blocks.
The "Frequency-Domain Filtering" and "Streaming" examples now use
a white noise and impulse signal, respectively.
1.6
Add "API Introduction" documentation section that was missing
from version 1.5, causing broken links.
Improve analysis and resynthesis performance when using PFFFT or vDSP
by automatically enabling the use of real rather than complex FFTs
where applicable.
1.5
Add navigation links to the HTML documentation.
Add a code example demonstrating synthesis of musical notes.
Add a function process() for iterating over coefficients sets with
greater flexibility than apply(). Also add a function fill() for
algorithmically creating new coefficients.
Make the C++ declarations in the API reference documents more closely
resemble actual C++ code.
Add a method gaborator::analyzer::band_ref() returning the band number
corresponding to the reference frequency.
1.4
Support building the library as C++17, while retaining compatibility
with C++11.
Further improve the performance of analyzing short signal blocks, and
of signal blocks not aligned to large powers of two.
Add a code example mesasuring the resynthesis signal-to-noise
ratio (SNR).
1.3
Eliminate some compiler warnings.
Declare gaborator::analyzer::band_ff() const, making the code match
the documentation.
Fix incorrect return type of gaborator::analyzer::band_ff() in the
documentation.
Improve performance of analyzing short signal blocks.
Remove special-case optimization of analyzing signal slices of all
zeros, as it caused incorrect results.
Support up to 384 bands per octave.
1.2
Add overview documentation.
Add real-time FAQ.
Actually include version.h in the release.
Fix off-by-one error in defintion of analyzer constructor ff_min
argument.
Fix incorrect return value of band_ff() for DC band.
Add streaming example code.
Add analyzer::analysis_support() and analyzer::synthesis_support().
Document analyzer::band_ff().
Improve signal to noise ratio at low numbers of bands per octave.
Note the need for -mfpu=neon on ARM in render.html.
1.1
Added CHANGES file.
Added reference documentation.
New include file gaborator/version.h.
1.0
Initial release

11
lib/gaborator/LICENSE Normal file
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The Gaborator library is Copyright (C) 1992-2019 Andreas Gustafsson.
License to distribute and modify the code is hereby granted under the
terms of the GNU Affero General Public License, version 3 (henceforth,
the AGPLv3), but not under other versions of the AGPL. See the file
doc/agpl-3.0.txt for the full text of the AGPLv3.
If the terms of the AGPLv3 are not acceptable to you, commercial
licensing under different terms is possible. Please contact
info@gaborator.com for more information.

1
lib/gaborator/README Normal file
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@ -0,0 +1 @@
See doc/index.html for HTML documentation.

661
lib/gaborator/doc/agpl-3.0.txt Normal file
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GNU AFFERO GENERAL PUBLIC LICENSE
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<html>
<head>
<link rel="stylesheet" href="doc.css" />
<title>Gaborator Example 2: Frequency-Domain Filtering</title>
</head>
<body>
<h1>Example 2: Frequency-Domain Filtering</h1>
<h2>Introduction</h2>
<p>This example shows how to apply a filter to an audio file using
the Gaborator library, by turning the audio into spectrogram
coefficients, modifying the coefficients, and resynthesizing audio
from them.</p>
<p>The specific filter implemented here is a 3 dB/octave lowpass
filter. This is sometimes called a <i>pinking filter</i> because it
can be used to produce pink noise from white noise. In practice, the
3 dB/octave slope is only applied above some minimum frequency, for
example 20 Hz, because otherwise the gain of the filter would approach
infinity as the frequency approaches 0, and the impulse response would
have to be infinitely wide.
</p>
<p>Since the slope of this filter is not a multiple of 6 dB/octave, it
is difficult to implement as an analog filter, but by filtering
digitally in the frequency domain, arbitrary filter responses such as
this can easily be achieved.
</p>
<h2>Preamble</h2>
<pre>
#include &lt;memory.h&gt;
#include &lt;iostream&gt;
#include &lt;sndfile.h&gt;
#include &lt;gaborator/gaborator.h&gt;
int main(int argc, char **argv) {
if (argc &lt; 3) {
std::cerr &lt;&lt; "usage: filter input.wav output.wav\n";
exit(1);
}
</pre>
<h2>Reading the Audio</h2>
<p>The code for reading the input audio file is identical to
that in <a href="render.html">Example 1</a>:</p>
<pre>
SF_INFO sfinfo;
memset(&amp;sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &amp;sfinfo);
if (! sf_in) {
std::cerr &lt;&lt; "could not open input audio file: "
&lt;&lt; sf_strerror(sf_in) &lt;&lt; "\n";
exit(1);
}
double fs = sfinfo.samplerate;
sf_count_t n_frames = sfinfo.frames;
sf_count_t n_samples = sfinfo.frames * sfinfo.channels;
std::vector&lt;float&gt; audio(n_samples);
sf_count_t n_read = sf_readf_float(sf_in, audio.data(), n_frames);
if (n_read != n_frames) {
std::cerr &lt;&lt; "read error\n";
exit(1);
}
sf_close(sf_in);
</pre>
<h2>Spectrum Analysis Parameters</h2>
<p>The spectrum analysis works much the same as in Example 1,
but uses slightly different parameters.
We use a larger number of frequency bands per octave (100)
to minimize ripple in the frequency response, and the
reference frequency argument is omitted as we don't care about the
exact alignment of the bands with respect to a musical scale.</p>
<pre>
gaborator::parameters params(100, 20.0 / fs);
gaborator::analyzer&lt;float&gt; analyzer(params);
</pre>
<h2>Precalculating Gains</h2>
<p>The filtering will be done by multiplying each spectrogram
coefficient with a frequency-dependent gain. To avoid having to
calculate the gain on the fly for each coefficient, which would
be slow, we will precalculate the gains into a vector <code>band_gains</code>
of one gain value per band, including one for the
special lowpass band that contains the frequencies from 0 to 20 Hz.</p>
<pre>
std::vector&lt;float&gt; band_gains(analyzer.bands_end());
</pre>
<p>First, we calculate the gains for the bandpass bands.
For a 3 dB/octave lowpass filter, the voltage gain needs to be
proportional to the square root of the inverse of the frequency.
To get the frequency of each band, we call the
<code>analyzer</code> method <code>band_ff()</code>, which
returns the center frequency of the band in units of the
sampling frequency. The gain is normalized to unity at 20 Hz.
</p>
<pre>
for (int band = analyzer.bandpass_bands_begin(); band &lt; analyzer.bandpass_bands_end(); band++) {
double f_hz = analyzer.band_ff(band) * fs;
band_gains[band] = 1.0 / sqrt(f_hz / 20.0);
}
</pre>
<p>The gain of the lowpass band is set to the the same value as the
lowest-frequency bandpass band, so that the overall filter gain
plateaus smoothly to a constant value below 20&nbsp;Hz.</p>
<pre>
band_gains[analyzer.band_lowpass()] = band_gains[analyzer.bandpass_bands_end() - 1];
</pre>
<h2>De-interleaving</h2>
<p>To handle stereo and other multi-channel audio files,
we will loop over the channels and filter each channel separately.
Since <i>libsndfile</i> produces interleaved samples, we first
de-interleave the current channel into a temporary vector called
<code>channel</code>:</p>
<pre>
for (sf_count_t ch = 0; ch &lt; sfinfo.channels; ch++) {
std::vector&lt;float&gt; channel(n_frames);
for (sf_count_t i = 0; i &lt; n_frames; i++)
channel[i] = audio[i * sfinfo.channels + ch];
</pre>
<h2>Spectrum Analysis</h2>
<p>Now we can spectrum analyze the current channel, producing
a set of coefficients:</p>
<pre>
gaborator::coefs&lt;float&gt; coefs(analyzer);
analyzer.analyze(channel.data(), 0, channel.size(), coefs);
</pre>
<h2>Filtering</h2>
<p>
The filtering is done using the function
<code>process()</code>, which applies a user-defined function
to each spectrogram coefficient. Here, that user-defined function is a
lambda expression that multiplies the coefficient by the appropriate
precalculated frequency-dependent gain, modifying the coefficient in
place. The unused <code>int64_t</code> argument is the time in units
of samples; this could be use to implement a time-varying filter if
desired.</p>
<p>
The second and third argument to <code>process()</code> specify a
range of frequency bands to process; here we pass <code>INT_MIN,
INT_MAX</code> to process all of them. Similarly, the fourth and
fifth argument specify a time range to process, and we pass
<code>INT64_MIN, INT64_MAX</code> to process all the coefficients
in <code>coefs</code> regardless of time.
</p>
<pre>
process([&amp;](int band, int64_t, std::complex&lt;float&gt; &amp;coef) {
coef *= band_gains[band];
},
INT_MIN, INT_MAX,
INT64_MIN, INT64_MAX,
coefs);
</pre>
<h2>Resynthesis</h2>
<p>We can now resynthesize audio from the filtered coefficients by
calling <code>synthesize()</code>. This is a mirror image of the call to
<code>analyze()</code>: now the coefficients are the input, and
the buffer of samples is the output. The <code>channel</code>
vector that originally contained the input samples for the channel
is now reused to hold the output samples.</p>
<pre>
analyzer.synthesize(coefs, 0, channel.size(), channel.data());
</pre>
<h2>Re-interleaving</h2>
<p>The <code>audio</code> vector that contained the
original interleaved audio is reused for the interleaved
filtered audio. This concludes the loop over the channels.
</p>
<pre>
for (sf_count_t i = 0; i &lt; n_frames; i++)
audio[i * sfinfo.channels + ch] = channel[i];
}
</pre>
<h2>Writing the Audio</h2>
<p>The filtered audio is written using <i>libsndfile</i>,
using code that closely mirrors that for reading.
Note that we use <code>SFC_SET_CLIPPING</code>
to make sure that any samples too loud for the file format
will saturate; by default, <i>libsndfile</i> makes them
wrap around, which sounds really bad.</p>
<a name="writing_audio_code">
<pre>
SNDFILE *sf_out = sf_open(argv[2], SFM_WRITE, &amp;sfinfo);
if (! sf_out) {
std::cerr &lt;&lt; "could not open output audio file: "
&lt;&lt; sf_strerror(sf_out) &lt;&lt; "\n";
exit(1);
}
sf_command(sf_out, SFC_SET_CLIPPING, NULL, SF_TRUE);
sf_count_t n_written = sf_writef_float(sf_out, audio.data(), n_frames);
if (n_written != n_frames) {
std::cerr &lt;&lt; "write error\n";
exit(1);
}
sf_close(sf_out);
</pre>
</a>
<h2>Postamble</h2>
<p>
We need a couple more lines of boilerplate to make the example a
complete program:
</p>
<pre>
return 0;
}
</pre>
<h2>Compiling</h2>
<p>Like <a href="render.html#compiling">Example 1</a>, this example
can be built using a one-line build command:
</p>
<pre class="build Darwin Linux NetBSD FreeBSD">
c++ -std=c++11 -I.. -O3 -ffast-math `pkg-config --cflags sndfile` filter.cc `pkg-config --libs sndfile` -o filter
</pre>
<p>Or using the vDSP FFT on macOS:</p>
<pre class="build Darwin">
c++ -std=c++11 -I.. -O3 -ffast-math -DGABORATOR_USE_VDSP `pkg-config --cflags sndfile` filter.cc `pkg-config --libs sndfile` -framework Accelerate -o filter
</pre>
<p>Or using PFFFT (see <a href="render.html#compiling">Example 1</a> for how to download and build PFFFT):</p>
<pre class="build">
c++ -std=c++11 -I.. -Ipffft -O3 -ffast-math -DGABORATOR_USE_PFFFT `pkg-config --cflags sndfile` filter.cc pffft/pffft.o pffft/fftpack.o `pkg-config --libs sndfile` -o filter
</pre>
<h2>Running</h2>
<p>Running the following shell commands will download an example
audio file containing five seconds of white noise and filter it,
producing pink noise.</p>
<pre class="run">
wget http://download.gaborator.com/audio/white_noise.wav
./filter white_noise.wav pink_noise.wav
</pre>
<h2>Frequency response</h2>
<p>The following plot shows the actual measured frequency response of the
filter, with the expected 3 dB/octave slope above 20&nbsp;Hz and minimal
ripple:</p>
<img src="filter-response.png" alt="Frequency response plot" data-autogen="no">
<div class="nav"><span class="prev"><a href="render.html">Previous: Example 1: Rendering a Spectrogram Image</a></span><span class="next"><a href="stream.html">Next: Example 3: Streaming</a></span></div>
</body>
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<!DOCTYPE html>
<!--
Copyright (C) 2018-2021 Andreas Gustafsson. This file is part of
the Gaborator library source distribution. See the file LICENSE at
the top level of the distribution for license information.
-->
<html>
<head>
<link rel="stylesheet" href="doc.css" />
<link rel="icon" type="image/png" href="favicon64.png" />
<title>The Gaborator</title>
</head>
<body>
<h1>The Gaborator</h1>
<p>The Gaborator is a library that generates constant-Q spectrograms
for visualization and analysis of audio signals. It also supports a
fast and accurate inverse transformation of the spectrogram coefficients
back into audio for spectral effects and editing.</p>
<p>The Gaborator implements the invertible constant-Q transform of
Velasco, Holighaus, D&ouml;rfler, and Grill, described in the papers
<i><a href="http://www.univie.ac.at/nonstatgab/pdf_files/dohogrve11_amsart.pdf">
Constructing an invertible constant-Q transform with nonstationary Gabor frames, 2011</a></i>
and <i><a href="http://www.univie.ac.at/nonstatgab/pdf_files/dogrhove12_amsart.pdf">
A Framework for invertible, real-time constant-Q transforms, 2012</a></i>,
using Gaussian bandpass filters and an efficient multi-rate architecture.
</p>
<p>The Gaborator is written in C++11 and compatible with C++14 and C++17.
It has been tested on macOS, Linux, NetBSD, FreeBSD, and iOS, on Intel
x86_64 and ARM processors.</p>
<p>The Gaborator is open source under the GNU Affero General Public
License, version 3, and is also available for commercial licensing.
See the file <a href="../LICENSE">LICENSE</a> for details.</p>
<h2>Example Code</h2>
<p>The following examples demonstrate the use of the library in
various scenarios. They are presented in a "literate
programming" style, with the code embedded in the commentary
rather than the other way around.
Concatenating the code fragments in each example yields a complete C++
program, which can also be found as a <code>.cc</code> file in
the <code>examples/</code> directory.</p>
<ul>
<li><a href="render.html">Example 1: Rendering a Spectrogram Image</a></li>
<li><a href="filter.html">Example 2: Frequency-Domain Filtering</a></li>
<li><a href="stream.html">Example 3: Streaming</a></li>
<li><a href="snr.html">Example 4: Measuring the Signal-to-Noise Ratio</a></li>
<li><a href="synth.html">Example 5: Synthesis from Scratch</a></li>
</ul>
<h2>API Reference</h2>
<p>The following documents define the library API.
</p>
<ul>
<li><a href="ref/intro.html">API Introduction</a></li>
<li><a href="ref/gaborator_h.html">Spectrum analysis and synthesis: <code>gaborator.h</code></a></li>
<li><a href="ref/render_h.html">Spectrogram rendering: <code>render.h</code></a></li>
</ul>
<h2>How it Works</h2>
<p>The following document outlines the operation of the library.</p>
<ul>
<lI><a href="overview.html">Overview of Operation</a>
</ul>
<h2>FAQ</h2>
<ul>
<li><a href="realtime.html">Is it real-time?</a></li>
</ul>
<h2>Contact</h2>
<p>Email questions and bug reports to the author at info@gaborator.com.</p>
</body>
</html>

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<title>Overview of Operation</title>
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<body>
<h1>Overview of Operation</h1>
<p>The Gaborator performs three main functions:</p>
<ul>
<li>spectrum <i>analysis</i>, which turns a signal into a set
of <i>spectrogram coefficients</i>
<li><i>resynthesis</i> (aka <i>reconstruction</i>), which turns a
set of coefficients back into a signal, and
<li><i>rendering</i>, which
turns a set of coefficients into a rectangular array of
amplitude values that can be turned into pixels to display
a spectrogram.
</ul>
<p>The following sections give a high-level overview of each
of these functions.</p>
<h2>Analysis</h2>
<p>The first step of the analysis is to run the signal through
an <i>analysis filter bank</i>, to split it into a number of
overlapping frequency <i>bands</i>.</p>
<p>The filter bank consists of a number of logarithmically spaced
Gaussian bandpass filters and a single lowpass filter. Each bandpass
filter has a bandwidth proportional to its center frequency, which
means they all have the same quality factor Q and form
a <i>constant-Q</i> filter bank. The highest-frequency bandpass
filter will have a center frequency close to half the sample rate; in
the graphs below, this is simple labeled 0.5 because all frequencies
in the Gaborator are in units of the sample rate. The
lowest-frequency bandpass filter should be centered at, or slightly
below, the lowest frequency of interest to the application at hand.
For example, when analyzing audio, this is often the lower limit of
human hearing; at a sample rate of 44100 Hz, this means 20 Hz / 44100
Hz &asymp; 0.00045. This lower frequency limit is referred to as
the <i>minimum frequency</i> or f<sub>min</sub>.
</p>
<p>Although frequencies below f<sub>min</sub> are assumed to not be of
interest, they nonetheless need to be preserved to achieve perfect
reconstruction, and that is what the lowpass filter is for. Together,
the lowpass filter and the bandpass filters overlap to cover the full
frequency range from 0 to 0.5.</P>
<p>The spacing of the bandpass filters is specified by the user as an
integer number of filters (or, equivalently, bands) per octave. For
example, when analyzing music, this is often 12 bands per octave (one
band per semitone in the equal-tempered scale), or if a finer
frequency resolution is needed, some multiple of 12.</p>
<p>The following plot shows the frequency responses of the analysis
filters at 12 bands per octave and f<sub>min</sub> = 0.03. A more
typical f<sub>min</sub> for audio work would be 0.00045, but
that would make the plot hard to read because both the lowpass filter
and the lowest-frequency bandpass filters would be extremely narrow.</p>
<img src="gen/allkernels_v1_bpo12_ffmin0.03_ffref0.5_anl_wob.png" alt="Analysis filters">
<p>The output of each bandpass filter is shifted down in frequency to
a complex quadrature baseband. The baseband signal is then resampled
at a reduced sample rate, lower than that of the orignal signal but
high enough that there is negligible aliasing given the bandwidth of
the filter in case. The Gaborator uses sample rates related to the
original signal sample rate by powers of two. This means some of
frequency bands are sampled a bit more often than strictly
necessary, but has the advantage that the sampling can be synchronized
to make the samples of many frequency bands coincide in time, which
can be convenient in later analysis or spectrogram rendering. The
complex samples resulting from this process are the spectrogram
coefficients.</p>
<p>The center frequencies of the analysis filters and the points in
time at which they are sampled form a two-dimensional,
multi-resolution <i>time-frequency grid</i>, where high frequencies
are sampled sparsely in frequency but densely in time, and low
frequencies are sampled densely in frequency but sparsely in time.</p>
<p>The following plot illustrates the time-frequency sampling grid
corresponding to the parameters used in the previous plot. Note that
frequency was the X axis in the previous plot, but is the Y axis
here. The plot covers a time range of 128 signal samples, but
conceptually, the grid extends arbitrarily far in time, in both the
positive and the negative direction.</p>
<img src="gen/grid_v1_bpo12_ffmin0.03_ffref0.5_wob.png" alt="Sampling grid">
<h2>Resynthesis</h2>
<p>Resynthesizing a signal from the coefficients is more or less the
reverse of the analysis process. The coefficients are frequency
shifted from the complex baseband back to their original center
frequencies and run through a <i>reconstruction filter bank</i>
that is a <i>dual</i> of the analysis filter bank. The following
plot shows the frequency responses of the reconstruction filters
corresponding to the analysis filters shown earlier.</p>
<img src="gen/allkernels_v1_bpo12_ffmin0.03_ffref0.5_syn_wob.png" alt="Reconstruction filters">
<p>Although the bandpass filters may look similar to the Gaussian
filters of the analysis filter bank, their shapes are actually subtly
different.</p>
<h2>Spectrogram Rendering</h2>
<p>Rendering a spectrogram image from the coefficients involves
taking the magnitude of each complex coefficient, and then
resampling the resulting multi-resolution grid of magnitudes
into an evenly spaced pixel grid.</p>
<p>Because the coefficient sample rate varies by frequency band, the
resampling required in the horizontal (time) direction also varies.
Typically, the high-frequency bands of an audio spectrogram have more
than one coefficient per pixel and require downsampling (decimation),
some bands in the mid-range frequencies have a one-to-one relationship
between coefficients and pixels, and the low-frequency bands
have more than one pixel per coefficient and require upsampling
(interpolation).</p>
<div class="nav"><span class="prev"><a href="ref/render_h.html">Previous: Spectrogram rendering: <code>render.h</code></a></span><span class="next"><a href="realtime.html">Next: Is it real-time?</a></span></div>
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<h1>Is it real-time?</h1>
<p>Several people have asked whether the Gaborator is suitable for
real-time applications. There is no simple yes or no answer to
this question, because there are many different definitions of
"real-time", and the answer will depend the definition.
Below are some answers to the question "is it real-time?"
rephrased in terms of different definitions.</p>
<h2>Can it processes a recording in less time than its duration?</h2>
<p>Yes. For example, at 48 frequency bands per
octave, a single core of a 2.5 GHz Intel Core i5 CPU can analyze some
10 million samples per second, which is more than 200 times faster
than real time for a single channel of 44.1&nbsp;kHz audio.</p>
<h2>Does it have bounded latency?
Can it start producing output before consuming the entire input?
Will it stream?</h2>
<p>Yes. See the <a href="stream.html">streaming example</a>.
<h2>Does it have low latency?</h2>
<p>Probably not low enough for applications such as live musical
effects. The exact latency depends on factors such as the frequency
range and number of bands per octave, but tends to range between
"high" and "very high". For example, with the parameters used in the
online demo, 48 frequency bands per octave down to 20 Hz, the latency
of the analysis side alone is some 3.5 seconds, and if you do
analysis followed by resynthesis, the total latency will
be almost 13 seconds.</p>
<p>This can be reduced by choosing the analysis parameters for low latency.
For example, if you decrease the number of frequency bands per octave to 12,
and increase the minimum frequency to 200 Hz, the latency
will be about 85 milliseconds for analysis only, and about
300 milliseconds for analysis + resynthesis, but this is
still too much for a live effect.</p>
<p>Any constant-Q spectrum analysis involving low frequencies will
inherently have rather high latency (at least for musically useful
values of Q), because the lowest-frequency analysis filters will have
narrow bandwidths, which lead to long impulse responses. Furthermore,
the Gaborator uses symmetric Gaussian analysis filters that were
chosen for properties such as linear phase and accurate
reconstruction, not for low latency, so the latency will be higher
than what might be achievable with a constant-Q filter bank
specifically designed for low latency.</p>
<p>The latency only affects <i>causal</i> applications, and
arises from the need to wait for the arrival of future input samples
needed to calculate the present output, and not from the time it takes
to perform the calculations. In a non-causal application,
such as applying an effect to a recording, the latency does not apply,
and performance is limited only by the speed of the calculations.
This can lead to the somewhat paradoxical situation that applying an
effect to a live stream causes a latency of several seconds, but
applying the same effect to an entire one-minute recording runs in a
fraction of a second.</p>
<p>In analysis and visualization applications that don't need to
perform resynthesis, it is possible to partly hide the latency by
taking advantage of the fact that the coefficients for the higher
frequencies exhibit lower latency than those for low frequencies.
For example, a live spectrogram display could update the
high-frequency parts of the display before the corresponding
low-frequency parts. Alternatively, low-frequency parts of the
spectrogram may be drawn multiple times, effectively animating
the display of the low-frequency coefficients as they converge to
their final values. This approach can be seen in action in
the <a href="https://waxingwave.com/spectrolite/">Spectrolite</a>
iOS app.</p>
<h2>Does it support small blocks sizes?</h2>
<p>Yes, but there is a significant performance penalty.
The Gaborator works most efficiently when the signal is processed
in large blocks, preferably 2<sup>17</sup> samples or more,
corresponding to several seconds of signal at typical audio sample
rates.</p>
<p>A real-time application aiming for low latency will want to
use smaller blocks, for examples 2<sup>5</sup> to 2<sup>10</sup>
samples, and processing these will be significantly slower.
For example, as of version 1.4, analyzing a signal in blocks of
2<sup>10</sup> samples takes roughly five times as much CPU as
analyzing it in blocks of 2<sup>20</sup> samples.</p>
<p>For sufficiently small blocks, the processing time will exceed the
duration of the signal, at which point the system can no longer be
considered real-time. For example, analyzing a 48&nbsp;kHz audio
stream on a 2.5 GHz Intel Core i5 CPU, this happens at block sizes
below about 2<sup>4</sup> = 16 samples.</p>
<p>The resynthesis code is currently less optimized for small block
sizes than the analysis code, so the performance penalty for
resynthesizing small blocks is even greater than for analyzing small
blocks.</p>
<h2>Can it process a signal stream of any length?</h2>
<p>Not in practice &mdash; the length is limited by floating point
precision. At typical audio sample rates, roundoff errors start to
become significant after some hours.</p>
<h2>Does it avoid dynamic memory allocation in the audio processing path?</h2>
<p>Currently, no &mdash; it dynamically allocates both the coefficient data
structures and various temporary buffers.</p>
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<h1>Gaborator reference: <code>gaborator.h</code></h1>
<h2>Spectrum Analysis Parameters</h2>
<p>A <code>parameters</code> object holds a set of parameters that
determine the frequency range and resolution of the spectrum
analysis.</p>
<pre>
class parameters {
</pre>
<div class="class_def">
<h3>Constructor</h3>
<pre>
parameters(unsigned int bands_per_octave,
double ff_min,
double ff_ref = 1.0);
</pre>
<dl>
<dt><code>bands_per_octave</code></dt>
<dd>The number of frequency bands per octave.
Values from 4 to 384 (inclusive) are supported.
</dd>
<dt><code>ff_min</code></dt>
<dd>The lower limit of the analysis frequency range, in units of the
sample rate. The analysis filter bank will extend low enough in
frequency that <code>ff_min</code> falls between the two lowest
frequency bandpass filters.
Values from 0.001 to 0.13 are supported.</dd>
<dt><code>ff_ref</code></dt>
<dd>The reference frequency, in units of the sample rate.
This allows fine-tuning of the analysis and synthesis filter
banks such that the center frequency of one of the filters
is aligned with <code>ff_ref</code>. If <code>ff_ref</code>
falls outside the frequency range of the bandpass filter bank, this
works as if the range were extended to include
<code>ff_ref</code>. Must be positive. A typical value
when analyzing music is <code>440.0 / fs</code>, where
<code>fs</code> is the sample rate in Hz.
</dd>
</dl>
<h3>Comparison</h3>
<p>
Comparison operators are provided for compatibility with
standard container classes. The ordering is arbitrary but consistent.
</p>
<pre>
bool operator<(const parameters &amp;rhs) const;
bool operator==(const parameters &amp;rhs) const;
</pre>
</div>
<pre>
};
</pre>
<h2>Spectrogram Coefficients</h2>
<pre class="forward_decl">
template&lt;class T&gt; class analyzer;
</pre>
<p>
A <code>coefs</code> object stores a set of spectrogram coefficients.
It is a dynamic data structure and will be automatically grown to
accommodate new time ranges, for example as newly recorded audio is analyzed.
The template argument <code>T</code>
must match that of the <code>analyzer</code> (usually <code>float</code>).
The template argument <code>C</code> is the data type used to store each
coefficient value; there is usually no need to specify it explicitly as
it will default to <code>std::complex&lt;T&gt;</code>.
</p>
<pre>
template&lt;class T, class C = std::complex&lt;T&gt&gt;
class coefs {
</pre>
<div class="class_def">
<h3>Constructor</h3>
<pre>
coefs(analyzer&lt;T&gt; &amp;a);
</pre>
<p>
Construct an empty set of coefficients for use with the spectrum
analyzer <code>a</code>. This represents a signal that is zero
at all points in time.
</p>
</div>
<pre>
};
</pre>
<h2>Spectrum Analyzer</h2>
<p>
The <code>analyzer</code> object performs spectrum analysis and/or resynthesis
according to the given parameters. The template argument <code>T</code> is
the floating-point type to use for the calculations. This is typically <code>float</code>;
alternatively, <code>double</code> can be used for increased accuracy at the
expense of speed and memory consumption.</p>
<pre>template&lt;class T&gt;
class analyzer {</pre>
<div class="class_def">
<h3>Constructor</h3>
<pre>
analyzer(const parameters &amp;params);
</pre>
<dl>
<dt><code>params</code></dt>
<dd>The spectrum analysis parameters.
</dl>
<h3>Analysis and synthesis</h3>
<pre>
void
analyze(const T *signal,
int64_t t0,
int64_t t1,
coefs&lt;T&gt; &amp;coefs) const;
</pre>
<p>Spectrum analyze the samples at <code>*signal</code> and add the
resulting coefficients to <code>coefs</code>.
<dl>
<dt><code>signal</code></dt>
<dd>The signal samples to analyze, beginning with the sample from time <code>t0</code>
and ending with the last sample before time <code>t1</code>, for a total of
<code>t1 - t0</code> samples.
<dt><code>t0</code></dt>
<dd>The point in time when the sample at <code>signal[0]</code> was taken,
in samples. For example, when analyzing an audio recording, this is typically
0 for the first sample in the recording, but this reference point is arbitrary,
and negative times are valid. Accuracy begins to successively decrease
outside the range of about &plusmn;10<sup>8</sup> samples, so using
large time values should be avoided when they are not necessary because
of the length of the track.
</dd>
<dt><code>t1</code></dt>
<dd>The point in time of the sample one past the
end of the array of samples at <code>signal</code>,
in samples.
</dd>
<dt><code>coefs</code></dt><dd>The coefficient object that the results of the
spectrum analysis are added to.
</dl>
<p>If the <code>coefs</code> object already contains some
coefficients, the new coefficients are summed to those already
present. Because the analysis is a linear operation, this allows a
signal to be analyzed in blocks, by making multiple calls
to <code>analyze()</code> with non-overlapping ranges that together
cover the entire signal. For efficiency, the blocks should
be large, as in
<code>analyze(first_131072_samples, 0, 131072, coefs)</code>,
<code>analyze(next_131072_samples, 131072, 262144, coefs)</code>,
etc.
</p>
<pre>
void
synthesize(const coefs&lt;T&gt; &amp;coefs,
uint64_t t0,
uint64_t t1,
T *signal) const;
</pre>
<p>Synthesize signal samples from the coefficients <code>coef</code> and store
them at <code>*signal</code>.
</p>
<dl>
<dt><code>coefs</code></dt><dd>The coefficients to synthesize the signal from.</dd>
<dt><code>t0</code></dt>
<dd>The point in time of the first sample to synthesize,
in samples, using the same time scale as in <code>analyze()</code>.</dd>
<dt><code>t1</code></dt>
<dd>The point in time of the sample one past the last one to synthesize.</dd>
<dt><code>signal</code></dt>
<dd>The synthesized signal samples will be written here,
beginning with the sample from time <code>t0</code> and
and ending with the last sample before time <code>t1</code>,
for a total of <code>t1 - t0</code> samples.</dd>
</dl>
<p>The time range <code>t0</code>...<code>t1</code> may extend outside
the range analyzed using <code>analyze()</code>, in which case the
signal is assumed to be zero in the un-analyzed range.</p>
<p>A signal may be synthesized in blocks by making multiple calls to
<code>analyze()</code> with different sample ranges. For efficiency,
the blocks should be large, and each <code>t0</code> should
be multiple of a large power of two.<p>
<h3>Frequency Band Numbering</h3>
<p>The frequency bands of the analysis filter bank are numbered by
nonnegative integers that increase towards lower (sic) frequencies.
There is a number of <i>bandpass bands</i> corresponding to the
logarithmically spaced bandpass analysis filters, from near 0.5
(half the sample rate) to
near f<sub>min</sub>, and a single <i>lowpass band</i> containing the
residual signal from frequencies below f<sub>min</sub>.
The numbering can be examined using the following methods:
</p>
<pre>
int bandpass_bands_begin() const;
</pre>
<p>
Return the smallest valid bandpass band number, corresponding to the
highest-frequency bandpass filter.</p>
<pre>
int bandpass_bands_end() const;
</pre>
<p>
Return the bandpass band number one past the highest valid bandpass
band number, corresponding to one past the lowest-frequency bandpass
filter.
</p>
<pre>
int band_lowpass() const;
</pre>
<p>
Return the band number of the lowpass band.
</p>
<pre>
int band_ref() const;
</pre>
<p>
Return the band number corresponding to the reference frequency
<code>ff_ref</code>. If <code>ff_ref</code> falls within
the frequency range of the bandpass filter bank, this will
be a valid bandpass band number, otherwise it will not.
</p>
<pre>
double band_ff(int band) const;
</pre>
<p>
Return the center frequency of band number <i>band</i>, in units of the
sampling frequency.
</p>
<h3>Support</h3>
<pre>
double analysis_support() const;
</pre>
<p>Returns the one-sided worst-case time domain <i>support</i> of any of the
analysis filters. When calling <code>analyze()</code> with a sample at time <i>t</i>,
only spectrogram coefficients within the time range <i>t &plusmn; support</i>
will be significantly changed. Coefficients outside the range may change,
but the changes will sufficiently small that they may be ignored without
significantly reducing accuracy.</p>
<pre>
double synthesis_support() const;
</pre>
<p>Returns the one-sided worst-case time domain <i>support</i> of any of the
reconstruction filters. When calling <code>synthesize()</code> to
synthesize a sample at time <i>t</i>, the sample will only be
significantly affected by spectrogram coefficients in the time
range <i>t &plusmn; support</i>. Coefficients outside the range may
be used in the synthesis, but substituting zeroes for the actual
coefficient values will not significantly reduce accuracy.</p>
</div>
<pre>
};
</pre>
<h2>Functions</h2>
<h3>Iterating Over Existing Coefficients</h3>
<pre>
template &lt;class T, class F, class C0, class... CI&gt;
void process(F f,
int b0,
int b1,
int64_t t0,
int64_t t1,
coefs&lt;T, C0&gt; &amp;coefs0,
coefs&lt;T, CI&gt;&amp;... coefsi);
</pre>
<p>
Process one or more coefficient sets <code>coefs0</code>... by applying
the function <code>f</code> to each coefficient present in <code>coefs0</code>,
in an indeterminate order.</p>
</p>
<p>This can be optionally limited to coefficients whose
band number <i>b</i> and sample time <i>t</i> satisfy
<code>b0</code> &leq; <i>b</i> &lt; <code>b1</code> and
<code>t0</code> &leq; <i>t</i> &lt; <code>t1</code>.
To process every coefficient present
in <code>coefs0</code>, pass <code>INT_MIN, INT_MAX, INT64_MIN, INT64_MAX</code>
for the arguments <code>b0</code>, <code>b1</code>, <code>t0</code>,
and <code>t1</code>, respectively.
</p>
<p>The function <code>f</code> should have the call signature</p>
<dd>
<pre>
template&lt;class T&gt;
void f(int b, int64_t t, std::complex&lt;T&gt; &c0, std::complex&lt;T&gt; &ci...);
</pre>
<p>where</p>
<dl>
<dt><code>b</code></dt>
<dd>The band number of the frequency band the coefficients
<code>c0</code> and <code>ci...</code> pertain to.
This may be either a bandpass band or the lowpass band.</dd>
<dt><code>t</code></dt>
<dd>The point in time the coefficients <code>c0</code> and
<code>ci...</code> pertain to, in samples</dd>
<dt><code>c0</code></dt>
<dd>A reference to a complex coefficient from <code>coefs0</code></dd>
<dt><code>ci...</code></dt>
<dd>Optional references to complex coefficients from the additional
coefficient sets <code>coefsi...</code>.</dd>
</dl>
</dd>
</dl>
<p>The function <code>f</code> may read and/or modify each of the
coefficients passed through <code>c0</code> and each
<code>ci...</code>.</p>
<p>The first coefficient set <code>c0</code> is a special case when
it comes to the treatment of missing values. Coefficients missing
from <code>c0</code> will not be iterated over at all, but when a
coefficient <i>is</i> iterated over and is missing from one of the additional
coefficient sets <code>ci...</code>, it will be automatically created
and initialized to zero in that additional coefficient set.</p>
<p><i>Note: The template parameters <code>C0</code>
and <code>CI</code>... exist to support the processing of coefficient
sets containing data of types other
than <code>std::complex&lt;T&gt;</code>, which is not currently part of the
documented API. In typical use, there is no need to specify them when
calling <code>apply()</code> because the template parameter list
can be deduced, but if they are expicitly specified, they should all
be <code>std::complex&lt;T&gt;</code>.
</i></p>
<h3>Creating New Coefficients</h3>
<pre>
template &lt;class T, class F, class C0, class... CI&gt;
void fill(F f,
int b0,
int b1,
int64_t t0,
int64_t t1,
coefs&lt;T, C0&gt; &amp;coefs0,
coefs&lt;T, CI&gt;&amp;... coefsi);
</pre>
<p>
Fill a region of the time-frequency plane with coefficients
and apply the function <code>f</code> to each.
</p>
<p>This works like <code>process()</code> except that it is not limited
to processing coefficients that already exist in <code>coefs0</code>;
instead, any missing coefficients in <code>coefs0</code> as well as
any of the <code>coefsi</code>... are created and initialized to zero
before <code>f</code> is called.</p>
<p>The <code>t0</code> and <code>t1</code> arguments must specify an
explicit, bounded time range &mdash; they must not be given as
INT64_MIN and/or INT64_MAX as that would mean creating coefficients
for an an astronomically large time range, requiring a correspondingly
astronomical amount of memory.</p>
<h3>Forgetting Coefficients</h3>
<pre>
template &lt;class T&gt;
void forget_before(const analyzer&lt;T&gt; &a,
coefs&lt;T&gt; &c,
int64_t limit);
</pre>
<p>Allow the coefficients for points in time before <code>limit</code>
(a time in units of samples) to be forgotten.
Streaming applications can use this to free memory used by coefficients
that are no longer needed. Coefficients that have been forgotten will
read as zero. This does not guarantee that all coefficients before
<code>limit</code> are forgotten, only that ones for
<code>limit</code> or later are not, and that the amount of memory
consumed by any remaining coefficients before <code>limit</code> is
bounded.</p>
<h3>Legacy API For Iterating Over Existing Coefficients</h3>
<p>Prior to version 1.5, the only way to iterate over
coefficients was the <code>apply()</code> function.
It is similar to <code>process()</code>, except that it
</p>
<ul>
<li>requires an additional <code>analyzer</code> argument,
<li>takes arguments in a different order,
<li>applies a function <code>f</code> taking arguments in a different order,
<li>does not support restricting the processing to a range of band numbers,
<li>only supports iterating over a single coefficient set, and
<li>provides default values for t0 and t1.
</ul>
<p>In new code, <code>process()</code> is preferred.</p>
<pre>
template &lt;class T, class F&gt;
void apply(const analyzer&lt;T&gt; &amp;a,
coefs&lt;T&gt; &amp;c,
F f,
int64_t t0 = INT64_MIN,
int64_t t1 = INT64_MAX);
</pre>
<p>
Apply the function <code>f</code> to each coefficient in the coefficient
set <code>c</code> for points in time <i>t</i> that satisfy
<code>t0</code> &leq; <i>t</i> &lt; <code>t1</code>.
If the <code>t0</code> and <code>t1</code> arguments are omitted, <code>f</code>
is applied to every coefficient.
</p>
<dl>
<dt><code>a</code></dt>
<dd>The spectrum analyzer that produced the coefficients <code>c</code></dd>
<dt><code>c</code></dt>
<dd>A set of spectrogram coefficients</dd>
<dt><code>f</code></dt>
<dd>A function to apply to each coefficient in <code>c</code>,
with the call signature
<pre>
template&lt;class T&gt;
void f(std::complex&lt;T&gt; &amp;coef, int band, int64_t t);
</pre>
<dl>
<dt><code>coef</code></dt>
<dd>A reference to a single complex coefficient. This may be read and/or modified.</dd>
<dt><code>band</code></dt>
<dd>The band number of the frequency band the coefficient <code>coef0</code> pertains to.
This may be either a bandpass band or the lowpass band.</dd>
<dt><code>t</code></dt>
<dd>The point in time the coefficient <code>c0</code> pertains to, in samples</dd>
<dt><code>t0</code></dt><dd>When not <code>INT64_MIN</code>, only apply <code>f</code> to the coefficients for time &ge; <code>t0</code></dd>
<dt><code>t1</code></dt><dd>When not <code>INT64_MAX</code>, only apply <code>f</code> to the coefficients for time &lt; <code>t1</code></dd>
</dl>
</dd>
</dl>
<div class="nav"><span class="prev"><a href="intro.html">Previous: API Introduction</a></span><span class="next"><a href="render_h.html">Next: Spectrogram rendering: <code>render.h</code></a></span></div>
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<head>
<link rel="stylesheet" href="../doc.css" type="text/css" />
<title>Gaborator reference: API Introdution</title>
</head>
<body>
<h1>Gaborator reference: API Introduction</h1>
<p>The public API of the Gaborator library is defined in the HTML
documentation in the form of annotated C++ declarations. These are
similar to the actual declarations in the respective header files, but
simplified for clarity and omitting implementation details.</p>
<p>The actual implementation in the header file may be different in a
number of ways but nonetheless compatible with the documented API.
For example, classes may be declared using the keyword <code>struct</code>
rather than <code>class</code>, function parameter names may be
different, types may be declared using different but equivalent
typedefs, and functions or templates in the header file may have
additional arguments with default values. Any classes, functions, and
other definitions not mentioned in the documentation should be
considered private and are subject to change or deletion without
notice.
</p>
<p>All definitions are in the namespace <code>gaborator</code>.
Applications need to either prefix class names
with <code>gaborator::</code>, or use <code>using namespace
gaborator;</code>.
</p>
<div class="nav"><span class="prev"><a href="../synth.html">Previous: Example 5: Synthesis from Scratch</a></span><span class="next"><a href="gaborator_h.html">Next: Spectrum analysis and synthesis: <code>gaborator.h</code></a></span></div>
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<head>
<link rel="stylesheet" href="../doc.css" type="text/css" />
<title>Gaborator reference: render.h</title>
</head>
<body>
<h1>Gaborator reference: <code>render.h</code></h1>
<h3>Spectrogram Rendering with Power-of-Two Scaling</h3>
<pre>
template &lt;class OI, class T&gt;
void render_p2scale(const analyzer&lt;T&gt; &amp;a,
const coefs&lt;T&gt; &amp;c,
int64_t xorigin, int64_t yorigin,
int64_t xi0, int64_t xi1, int xe,
int64_t yi0, int64_t yi1, int ye,
OI output);
</pre>
<p>Render a rectangular array of pixel values representing signal
amplitudes in time-frequency space, optionally scaling up or
down by powers of two.
</p>
<dl>
<dt><code>a</code></dt>
<dd>The spectrum analyzer that produced the coefficients <code>c</code></dd>
<dt><code>c</code></dt>
<dd>A set of spectrogram coefficients to render</dd>
<dt><code>xorigin</code></dt>
<dd>The point in time corresponding to pixel X coordinate 0, in samples</dd>
<dt><code>yorigin</code></dt>
<dd>The band number of the frequency band corresponding to pixel Y coordinate 0</dd>
<dt><code>xi0</code></dt>
<dd>The X coordinate of the first pixel to render</dd>
<dt><code>xi1</code></dt>
<dd>The X coordinate one past the last pixel to render</dd>
<dt><code>xe</code></dt>
<dd>The horizontal scaling exponent. One horizontal pixel corresponds to 2<sup>xe</sup> signal samples.</dd>
<dt><code>yi0</code></dt>
<dd>The Y coordinate of the first pixel to render</dd>
<dt><code>yi1</code></dt>
<dd>The Y coordinate one past the last pixel to render</dd>
<dt><code>ye</code></dt>
<dd>The vertical scaling exponent. One vertical pixel corresponds to 2<sup>ye</sup> frequency bands.</dd>
<dt><code>output</code></dt>
<dd>A random access iterator through which the output
pixel amplitude values will be written. This is
typically a <code>float *</code>. A total of
<code>(xi1 - xi0) * (yi1 - yi0))</code> values will be written.
</dd>
</dl>
<h3>Utility Functions</h3>
<pre>
template &lt;class T&gt;
unsigned int float2pixel_8bit(T amp);
</pre>
<p>Convert a normalized amplitude value to a 8-bit greyscale pixel value.</p>
<dl>
<dt><code>amp</code></dt>
<dd>A floating point value representing a signal amplitude, nominally ranging from 0 to 1</dd>
</dl>
<p>Returns an pixel value ranging from 0 to 255 (inclusive), using an
approximation of the sRGB gamma.</p>
<div class="nav"><span class="prev"><a href="gaborator_h.html">Previous: Spectrum analysis and synthesis: <code>gaborator.h</code></a></span><span class="next"><a href="../overview.html">Next: Overview of Operation</a></span></div>
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<html>
<head>
<link rel="stylesheet" href="doc.css" />
<title>Gaborator Example 1: Rendering a Spectrogram Image</title>
</head>
<body>
<h1>Example 1: Rendering a Spectrogram Image</h1>
<h2>Introduction</h2>
<p>This example shows how to generate a greyscale constant-Q
spectrogram image from an audio file using the Gaborator library.
</p>
<h2>Preamble</h2>
<p>We start off with some boilerplate #includes.</p>
<pre>
#include &lt;memory.h&gt;
#include &lt;iostream&gt;
#include &lt;fstream&gt;
#include &lt;sndfile.h&gt;
</pre>
<p>The Gaborator is a header-only library &mdash; there are no C++ files
to compile, only header files to include.
The core spectrum analysis and resynthesis code is in
<code>gaborator/gaborator.h</code>, and the code for rendering
images from the spectrogram coefficients is in
<code>gaborator/render.h</code>.</p>
<pre>
#include &lt;gaborator/gaborator.h&gt;
#include &lt;gaborator/render.h&gt;
</pre>
<p>The program takes the names of the input audio file and output spectrogram
image file as command line arguments, so we check that they are present:</p>
<pre>
int main(int argc, char **argv) {
if (argc &lt; 3) {
std::cerr &lt;&lt; "usage: render input.wav output.pgm\n";
exit(1);
}
</pre>
<h2>Reading the Audio</h2>
<p>The audio file is read using the <i>libsndfile</i> library
and stored in a <code>std::vector&lt;float&gt;</code>.
Note that although <i>libsndfile</i> is used in this example,
the Gaborator library itself does not depend on or
use <i>libsndfile</i>.</p>
<pre>
SF_INFO sfinfo;
memset(&amp;sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &amp;sfinfo);
if (! sf_in) {
std::cerr &lt;&lt; "could not open input audio file: "
&lt;&lt; sf_strerror(sf_in) &lt;&lt; "\n";
exit(1);
}
double fs = sfinfo.samplerate;
sf_count_t n_frames = sfinfo.frames;
sf_count_t n_samples = sfinfo.frames * sfinfo.channels;
std::vector&lt;float&gt; audio(n_samples);
sf_count_t n_read = sf_readf_float(sf_in, audio.data(), n_frames);
if (n_read != n_frames) {
std::cerr &lt;&lt; "read error\n";
exit(1);
}
sf_close(sf_in);
</pre>
<p>In case the audio file is a stereo or multi-channel one,
mix down the channels to mono, into a new <code>std::vector&lt;float&gt;</code>:
<pre>
std::vector&lt;float&gt; mono(n_frames);
for (size_t i = 0; i &lt; (size_t)n_frames; i++) {
float v = 0;
for (size_t c = 0; c &lt; (size_t)sfinfo.channels; c++)
v += audio[i * sfinfo.channels + c];
mono[i] = v;
}
</pre>
<h2>The Spectrum Analysis Parameters</h2>
<p>Next, we need to choose some parameters for the spectrum analysis:
the frequency resolution, the frequency range, and optionally a
reference frequency.</p>
<p>The frequency resolution is specified as a number of frequency
bands per octave. A typical number for analyzing music signals is 48
bands per octave, or in other words, four bands per semitone
in the 12-note equal tempered scale.</p>
<p>The frequency range is specified by giving a minimum frequency;
this is the lowest frequency that will be included in the spectrogram
display.
For audio signals, a typical minimum frequency is 20&nbsp;Hz,
the lower limit of human hearing. In the Gaborator library,
all frequencies are given in units of the sample rate rather
than in Hz, so we need to divide the 20&nbsp;Hz by the sample
rate of the input audio file: <code>20.0 / fs</code>.</p>
<p>Unlike the minimum frequency, the maximum frequency is not given
explicitly &mdash; instead, the analysis always produces coefficients
for frequencies all the way up to half the sample rate
(a.k.a. the Nyquist frequency). If you don't need the coefficients
for the highest frequencies, you can simply ignore them.</p>
<p>If desired, one of the frequency bands can be exactly aligned with
a <i>reference frequency</i>. When analyzing music signals, this is
typically 440 Hz, the standard tuning of the note <i>A<sub>4</sub></i>.
Like the minimum frequency, it is given in
units of the sample rate, so we pass <code>440.0 / fs</code>.</p>
<p>The parameters are held in an object of type
<code>gaborator::parameters</code>:
<pre>
gaborator::parameters params(48, 20.0 / fs, 440.0 / fs);
</pre>
<h2>The Spectrum Analyzer</h2>
<p>Next, we create an object of type <code>gaborator::analyzer</code>;
this is the workhorse that performs the actual spectrum analysis
(and/or resynthesis, but that's for a later example).
It is a template class, parametrized by the floating point type to
use for the calculations; this is typically <code>float</code>.
Constructing the <code>gaborator::analyzer</code> involves allocating and
precalculating all the filter coefficients and other auxiliary data needed
for the analysis and resynthesis, and this takes considerable time and memory,
so when analyzing multiple pieces of audio with the same
parameters, creating a single <code>gaborator::analyzer</code>
and reusing it is preferable to destroying and recreating it.</p>
<pre>
gaborator::analyzer&lt;float&gt; analyzer(params);
</pre>
<h2>The Spectrogram Coefficients</h2>
<p>The result of the spectrum analysis will be a set of <i>spectrogram
coefficients</i>. To store them, we will use a <code>gaborator::coefs</code>
object. Like the <code>analyzer</code>, this is a template class parametrized
by the data type. Because the layout of the coefficients is determined by
the spectrum analyzer, it must be passed as an argument to the constructor:</p>
<pre>
gaborator::coefs&lt;float&gt; coefs(analyzer);
</pre>
<h2>Running the Analysis</h2>
<p>Now we are ready to do the actual spectrum analysis,
by calling the <code>analyze</code> method of the spectrum
analyzer object.
The first argument to <code>analyze</code> is a <code>float</code> pointer
pointing to the first element in the array of samples to analyze.
The second and third arguments are of type
<code>int64_t</code> and indicate the time range covered by the
array, in units of samples. Since we are passing the whole file at
once, the beginning of the range is sample number zero, and the end is
sample number <code>mono.size()</code>. The fourth argument is a
reference to the set of coefficients that the results of the spectrum
analysis will be stored in.
</p>
<pre>
analyzer.analyze(mono.data(), 0, mono.size(), coefs);
</pre>
<h2>Rendering an Image</h2>
<p>Now there is a set of spectrogram coefficients in <code>coefs</code>.
To render them as an image, we will use the function
<code>gaborator::render_p2scale()</code>.
</p>
<p>Rendering involves two different coordinate
spaces: the time-frequency coordinates of the spectrogram
coefficients, and the x-y coordinates of the image.
The two spaces are related by an origin and a scale factor,
each with an x and y component.</p>
<p>The origin specifies the point in time-frequency space that
corresponds to the pixel coordinates (0, 0). Here, we will
use an origin where the x (time) component
is zero (the beginning of the signal), and the y (frequency) component
is the band number of the first (highest frequency) band:</p>
<pre>
int64_t x_origin = 0;
int64_t y_origin = analyzer.bandpass_bands_begin();
</pre>
<p><code>render_p2scale()</code> supports scaling the spectrogram in
both the time (horizontal) and frequency (vertical) dimension, but only
by power-of-two scale factors. These scale factors are specified
relative to a reference scale of one vertical pixel per frequency band
and one horizontal pixel per signal sample.
<p>Although a horizontal scale of one pixel per signal sample is a
mathematically pleasing reference point, this reference scale is not
used in practice because it would result in a spectrogram that is much
too stretched out horizontally. A more typical scale factor might be
2<sup>10</sup> = 1024, yielding one pixel for every 1024 signal
samples, which is about one pixel per 23 milliseconds of signal at a
sample rate of 44.1 kHz.</p>
<pre>
int x_scale_exp = 10;
</pre>
<p>To ensure that the spectrogram will fit on the screen even in the
case of a long audio file, let's auto-scale it down further until
it is no more than 1000 pixels wide:</p>
<pre>
while ((n_frames &gt;&gt; x_scale_exp) &gt; 1000)
x_scale_exp++;
</pre>
<p>In the vertical, the reference scale factor of one pixel per
frequency band is reasonable, so we will use it as-is. In other words,
the vertical scale factor will be 2<sup>0</sup>.</p>
<pre>
int y_scale_exp = 0;
</pre>
<p>Next, we need to define the rectangular region of the image
coordinate space to render. Since we are rendering the entire
spectrogram rather than a tile, the top left corner of the
rectangle will have an origin of (0, 0).
</p>
<pre>
int64_t x0 = 0;
int64_t y0 = 0;
</pre>
<p>The coordinates of the bottom right corner are determined by the
length of the signal and the number of bands, respectively, taking the
scale factors into account.
The length of the signal in samples is <code>n_frames</code>,
and we get the number of bands as the difference of the end points of
the range of band numbers:
<code>analyzer.bandpass_bands_end() - analyzer.bandpass_bands_begin()</code>.
The scale factor is taken into account by right shifting by the
scale exponent.
</p>
<pre>
int64_t x1 = n_frames &gt;&gt; x_scale_exp;
int64_t y1 = (analyzer.bandpass_bands_end() - analyzer.bandpass_bands_begin()) &gt;&gt; y_scale_exp;
</pre>
<p>The right shift by <code>y_scale_exp</code> above doesn't actually
do anything because <code>y_scale_exp</code> is zero, but it would be
needed if, for example, you were to change <code>y_scale_exp</code> to
1 to get a spectrogram scaled to half the height. You could also make a
double-height spectrogram by setting <code>y_scale_exp</code> to -1,
but then you also need to change the
<code>&gt;&gt; y_scale_exp</code> to
<code>&lt;&lt; -y_scale_exp</code> since you can't shift by
a negative number.
</p>
<p>We are now ready to render the spectrogram, producing
a vector of floating-point amplitude values, one per pixel.
Although this is stored as a 1-dimensional vector of floats, its
contents should be interpreted as a 2-dimensional rectangular array of
<code>(y1 - y0)</code> rows of <code>(x1 - x0)</code> columns
each, with the row indices increasing towards lower
frequencies and column indices increasing towards later
sampling times.
</p>
<pre>
std::vector&lt;float&gt; amplitudes((x1 - x0) * (y1 - y0));
gaborator::render_p2scale(
analyzer,
coefs,
x_origin, y_origin,
x0, x1, x_scale_exp,
y0, y1, y_scale_exp,
amplitudes.data());
</pre>
<h2>Writing the Image File</h2>
<p>To keep the code simple and to avoid additional library
dependencies, the image is stored in
<code>pgm</code> (Portable GreyMap) format, which is simple
enough to be generated with just a few lines of inline code.
Each amplitude value in <code>amplitudes</code> is converted into an 8-bit
gamma corrected pixel value by calling <code>gaborator::float2pixel_8bit()</code>.
To control the brightness of the resulting image, each
amplitude value is multiplied by a gain; this may have to be adjusted
depending on the type of signal and the amount of headroom in the
recording, but a gain of about 15 often works well for typical music
signals.</p>
<pre>
float gain = 15;
std::ofstream f;
f.open(argv[2], std::ios::out | std::ios::binary);
f << "P5\n" << (x1 - x0) << ' ' << (y1 - y0) << "\n255\n";
for (size_t i = 0; i < amplitudes.size(); i++)
f.put(gaborator::float2pixel_8bit(amplitudes[i] * gain));
f.close();
</pre>
<h2>Postamble</h2>
<p>
To make the example code a complete program,
we just need to finish <code>main()</code>:
</p>
<pre>
return 0;
}
</pre>
<a name="compiling"><h2>Compiling</h2></a>
<p>
If you are using macOS, Linux, NetBSD, or a similar system, you can build
the example by running the following command in the <code>examples</code>
subdirectory.
You need to have <i>libsndfile</i> is installed and supported by
<code>pkg-config</code>.
</p>
<pre class="build Darwin Linux NetBSD FreeBSD">
c++ -std=c++11 -I.. -O3 -ffast-math `pkg-config --cflags sndfile` render.cc `pkg-config --libs sndfile` -o render
</pre>
<h2>Compiling for Speed</h2>
<p>The above build command uses the Gaborator's built-in FFT implementation,
which is simple and portable but rather slow. Performance can be
significantly improved by using a faster FFT library. On macOS, you
can use the FFT from Apple's vDSP library by defining
<code>GABORATOR_USE_VDSP</code> and linking with the <code>Accelerate</code>
framework:
</p>
<pre class="build Darwin">
c++ -std=c++11 -I.. -O3 -ffast-math -DGABORATOR_USE_VDSP `pkg-config --cflags sndfile` render.cc `pkg-config --libs sndfile` -framework Accelerate -o render
</pre>
<p>On Linux and NetBSD, you can use the PFFFT (Pretty Fast FFT) library.
You can get the latest version from
<a href="https://bitbucket.org/jpommier/pffft">https://bitbucket.org/jpommier/pffft</a>,
or the exact version that was used for testing from gaborator.com:
</p>
<!-- ftp https://bitbucket.org/jpommier/pffft/get/29e4f76ac53b.zip -->
<pre class="build Linux NetBSD FreeBSD">
wget http://download.gaborator.com/mirror/pffft/29e4f76ac53b.zip
unzip 29e4f76ac53b.zip
mv jpommier-pffft-29e4f76ac53b pffft
</pre>
<p>Then, compile it:</p>
<pre class="build Linux NetBSD FreeBSD">
cc -c -O3 -ffast-math pffft/pffft.c -o pffft/pffft.o
</pre>
<p>(If you are building for ARM, you will need to add <code>-mfpu=neon</code> to
both the above compilation command and the ones below.)</p>
<p>PFFFT is single precision only, but it comes with a copy of FFTPACK which can
be used for double-precision FFTs. Let's compile that, too:</p>
<pre class="build Linux NetBSD FreeBSD">
cc -c -O3 -ffast-math -DFFTPACK_DOUBLE_PRECISION pffft/fftpack.c -o pffft/fftpack.o
</pre>
<p>Then build the example and link it with both PFFFT and FFTPACK:</p>
<pre class="build Linux NetBSD FreeBSD">
c++ -std=c++11 -I.. -Ipffft -O3 -ffast-math -DGABORATOR_USE_PFFFT `pkg-config --cflags sndfile` render.cc pffft/pffft.o pffft/fftpack.o `pkg-config --libs sndfile` -o render
</pre>
<h2>Running</h2>
<p>Running the following shell commands will download a short example
audio file (of picking each string on an acoustic guitar), generate
a spectrogram from it as a <code>.pgm</code> image, and then convert
the <code>.pgm</code> image into a <code>JPEG</code> image:
<pre class="run">
wget http://download.gaborator.com/audio/guitar.wav
./render guitar.wav guitar.pgm
cjpeg &lt;guitar.pgm &gt;guitar.jpg
</pre>
<h2>Example Output</h2>
<p>The JPEG file produced by the above will look like this:</p>
<img src="spectrogram.jpg" alt="Spectrogram" data-autogen="no">
<div class="nav"><span class="next"><a href="filter.html">Next: Example 2: Frequency-Domain Filtering</a></span></div>
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<link rel="stylesheet" href="doc.css" />
<title>Gaborator Example 4: Measuring the Signal-to-Noise Ratio</title>
</head>
<body>
<h1>Example 4: Measuring the Signal-to-Noise Ratio</h1>
<h2>Introduction</h2>
<p>This example measures the signal-to-noise ratio (SNR) of the
resynthesis by analyzing and resynthesizing a test signal
and comparing the resynthesis result to the original.
</p>
<p>Since it does not involve any audio file I/O, this example
does not require the sndfile library, making it the shortest
and simplest one by far.</p>
<h2>Preamble</h2>
<pre>
#include &lt;iostream&gt;
#include &lt;iomanip&gt;
#include &lt;random&gt;
#include &lt;gaborator/gaborator.h&gt;
</pre>
<h2>Amplitude Measurement</h2>
<p>To calculate the signal-to-noise ratio, we need to measure the
amplitude of the orignal signal and the error residue. We will use
the root-mean-square amplitude, which is calculcated by the
function <code>rms()</code>.
</p>
<pre>
double rms(const std::vector&lt;float&gt; &amp;v) {
double sqsum = 0;
for (size_t i = 0; i &lt; v.size(); i++) {
sqsum += v[i] * v[i];
}
return sqrt(sqsum);
}
</pre>
<h2>Main Program</h2>
<p>For the test signal, we use a million samples of white noise with a
uniform amplitude distribution between -1 and +1.</p>
<pre>
int main(int argc, char **argv) {
size_t len = 1000000;
std::vector&lt;float&gt; signal_in(len);
std::minstd_rand rand;
std::uniform_real_distribution&lt;&gt; uniform(-1.0, 1.0);
for (size_t i = 0; i &lt; len; i++)
signal_in[i] = uniform(rand);
</pre>
<p>Then we create a spectrum analyzer with 48 bands per octave
and a frequency range of 3 decades (0.0005 to 0.5 times the sample rate):</p>
<pre>
gaborator::parameters params(48, 5e-4);
gaborator::analyzer&lt;float&gt; analyzer(params);
</pre>
<p>...and run the spectrum analyzis:</p>
<pre>
gaborator::coefs&lt;float&gt; coefs(analyzer);
analyzer.analyze(signal_in.data(), 0, len, coefs);
</pre>
<p>...resynthesize the signal into <code>signal_out</code>:
<pre>
std::vector&lt;float&gt; signal_out(len);
analyzer.synthesize(coefs, 0, len, signal_out.data());
</pre>
<p>...measure the resynthesis error:</p>
<pre>
std::vector&lt;float&gt; error(len);
for (size_t i = 0; i &lt; len; i++)
error[i] = signal_out[i] - signal_in[i];
</pre>
<p>...calculate the signal-to-noise ratio:</p>
<pre>
double snr = rms(signal_in) / rms(error);
</pre>
<p>...and print it in decibels:</p>
<pre>
std::cout << std::fixed << std::setprecision(1) << 20 * log10(snr) << " dB\n";
}
</pre>
<h2>Compiling</h2>
<p>Like <a href="render.html#compiling">Example 1</a>, this example
can be built using a one-line build command:
</p>
<pre class="build Darwin Linux NetBSD FreeBSD">
c++ -std=c++11 -I.. -O3 -ffast-math `pkg-config --cflags sndfile` snr.cc `pkg-config --libs sndfile` -o snr
</pre>
<p>Or using the vDSP FFT on macOS:</p>
<pre class="build Darwin">
c++ -std=c++11 -I.. -O3 -ffast-math -DGABORATOR_USE_VDSP `pkg-config --cflags sndfile` snr.cc `pkg-config --libs sndfile` -framework Accelerate -o snr
</pre>
<p>Or using PFFFT (see <a href="render.html#compiling">Example 1</a> for how to download and build PFFFT):</p>
<pre class="build">
c++ -std=c++11 -I.. -Ipffft -O3 -ffast-math -DGABORATOR_USE_PFFFT `pkg-config --cflags sndfile` snr.cc pffft/pffft.o pffft/fftpack.o `pkg-config --libs sndfile` -o snr
</pre>
<h2>Running</h2>
<p>The program is run with no arguments:</p>
<pre class="run">
./snr
</pre>
<p>This will print the SNR which should be more than 100 dB if the library is working correctly.</p>
<div class="nav"><span class="prev"><a href="stream.html">Previous: Example 3: Streaming</a></span><span class="next"><a href="synth.html">Next: Example 5: Synthesis from Scratch</a></span></div>
</body>
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<!DOCTYPE html>
<!--
Copyright (C) 2018-2020 Andreas Gustafsson. This file is part of
the Gaborator library source distribution. See the file LICENSE at
the top level of the distribution for license information.
-->
<html>
<head>
<link rel="stylesheet" href="doc.css" />
<title>Gaborator Example 3: Streaming</title>
</head>
<body>
<h1>Example 3: Streaming</h1>
<h2>Introduction</h2>
<p>This example shows how to process streaming audio a block at a time,
rather than operating on a complete recording at once as in the previous
examples.</p>
<p>This program doesn't do anything particulary useful &mdash; it just
inverts the phase of the signal, but not using the obvious method of
changing the sign of each sample but by changing the sign of each
spectrogram coefficient. Consider the expression <code>coef =
-coef</code> a placeholder for your own streaming filter or effect
code.</p>
<h2>Preamble</h2>
<pre>
#include &lt;memory.h&gt;
#include &lt;iostream&gt;
#include &lt;sndfile.h&gt;
#include &lt;gaborator/gaborator.h&gt;
int main(int argc, char **argv) {
if (argc &lt; 3) {
std::cerr &lt;&lt; "usage: stream input.wav output.wav\n";
exit(1);
}
</pre>
<h2>Opening the Streams</h2>
<p>We again use <i>libsndfile</i> to read the input and write the output.
To keep it simple, this example only handles mono files.</p>
<pre>
SF_INFO sfinfo;
memset(&amp;sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &amp;sfinfo);
if (! sf_in) {
std::cerr &lt;&lt; "could not open input audio file: "
&lt;&lt; sf_strerror(sf_in) &lt;&lt; "\n";
exit(1);
}
if (sfinfo.channels != 1) {
std::cerr &lt;&lt; "only mono files are supported\n";
exit(1);
}
double fs = sfinfo.samplerate;
SNDFILE *sf_out = sf_open(argv[2], SFM_WRITE, &amp;sfinfo);
if (! sf_out) {
std::cerr &lt;&lt; "could not open output audio file: "
&lt;&lt; sf_strerror(sf_out) &lt;&lt; "\n";
exit(1);
}
</pre>
<p>The next couple of lines work around a design flaw in
<i>libsndfile</i>. By default, when reading a 16-bit
audio file as floating point data and then writing them
as another 16-bit audio file, <i>libsndfile</i> will use slightly
different scale factors on input and output, and the output will
not be bit-identical to the input. To make it easier to verify
that this example actually yields correct results to within
the full 16-bit precision, we select a non-normalized floating
point representation, which does not suffer from this flaw.</p>
<pre>
sf_command(sf_in, SFC_SET_NORM_FLOAT, NULL, SF_FALSE);
sf_command(sf_out, SFC_SET_NORM_FLOAT, NULL, SF_FALSE);
</pre>
<h2>Spectrum Analysis Parameters</h2>
<p>As in Example 1, the parameters are chosen for analyzing music, but
to reduce the latency, the number of frequency bands per octave is reduced
from 48 to 12 (one per semitone), and the lower frequency limit of
the bandpass filter bank is raised from 20&nbsp;Hz to 200&nbsp;Hz.</p>
<pre>
gaborator::parameters params(12, 200.0 / fs, 440.0 / fs);
gaborator::analyzer&lt;float&gt; analyzer(params);
</pre>
<h2>Calculating Latency</h2>
<p>The spectrogram coefficients are calculated by applying symmetric
FIR filters to the audio signal. This means a spectrogram coefficient
for any given point in time <i>t</i> is a weighted average of samples
from both before and after <i>t</i>, representing both past and future
signal. The width of the filter impulse response depends on the
bandwidth, which in turn depends on the center frequency of its band.
The lowest-frequency filters have the narrowest bandwidths, and
therefore the widest impulses response, and need the greatest amount
of past and future signal. The width of the filter impulse response
is called its <i>support</i>, and the worst-case (widest) support of
any analysis filter can be found by calling the function
<code>gaborator::analyzer::analysis_support()</code>. This returns
the <i>one-sided</i> support, the width of the impulse
response <i>to each side</i> of its center, as a floating point number.
To be on the safe side, let's round this up to the next integer:</p>
<pre>
size_t analysis_support = ceil(analyzer.analysis_support());
</pre>
<p>Similarly, when resynthesizing audio from coefficients, calculating
a sample at time <i>t</i> involves applying symmetric FIR
reconstruction filters, calculating a weighted average of both past and
future spectrogram coefficients. The support of the widest reconstruction
filter can be calculated by calling
<code>gaborator::analyzer::synthesis_support()</code>:
</p>
<pre>
size_t synthesis_support = ceil(analyzer.synthesis_support());
</pre>
<p>In a real-time application, the need to access future signal
samples and/or coefficients causes latency. A real-time audio
analysis application that needs to examine the coefficients for
time <i>t</i> can only do so when it has received the input samples up
to time <i>t + analysis_support</i>, and therefore has a minimum latency of
<i>analysis_support</i>. A real-time filtering or effect
application, such as the present example,
incurs latency from both analysis and reconstruction
filters, and can only produce the output sample for time <i>t</i> once
it has received the input samples up to
<i>t + analysis_support + synthesis_support</i>,
for a minimum latency of <i>analysis_support + synthesis_support</i>.
Let's print this total latency to standard output:
</p>
<pre>
std::cerr << "latency: " << analysis_support + synthesis_support << " samples\n";
</pre>
<p>In a practical real-time system, there will be additional latency
caused by processing the signal in blocks of samples rather than a
sample at a time. Since the block size is a property of the overall
system, and causes latency even if the Gaborator is not involved, that
latency is considered outside the scope of this discussion.
</p>
<h2>Streaming</h2>
<p>To mimic a typical real-time system, the audio is processed
in fixed-size blocks (here, 1024 samples). If the size
of the input file is not divisible by the block size, the last block
is padded with zeroes.
The variable <code>t_in</code> keeps track of time, indicating
the sampling time of the first sample of the current input block,
in units of samples.
</p>
<pre>
gaborator::coefs&lt;float&gt; coefs(analyzer);
const size_t blocksize = 1024;
std::vector&lt;float&gt; buf(blocksize);
int64_t t_in = 0;
for (;;) {
sf_count_t n_read = sf_readf_float(sf_in, buf.data(), blocksize);
if (n_read == 0)
break;
if (n_read < blocksize)
std::fill(buf.data() + n_read, buf.data() + blocksize, 0);
</pre>
<p>Now we can spectrum analyze the current block of samples. Note how
the time range,
<code>t_in</code>...<code>t_in + blocksize</code>,
is explicitly passed to <code>analyze()</code>.
</p>
<pre>
analyzer.analyze(buf.data(), t_in, t_in + blocksize, coefs);
</pre>
<p>The call to <code>analyze()</code> updates the coefficients
for the time range from <code>t_in - analysis_support</code> to
<code>t_in + blocksize + analysis_support</code>. The oldest
<code>blocksize</code> samples of this time range,
that is, from <code>t_in - analysis_support</code> to
<code>t_in - analysis_support + blocksize</code>, were now updated for
the last time and will not be affected by future input blocks.
Therefore, it is now safe to examine and/or modify these
coefficients as required by your application. Here, by way
of example, we simply change their signs to invert the phase of the signal.
Note that unlike the earlier filter example where <code>prorcess()</code>
applied a function to all the coefficients, here it is applied only to
the coefficients within a limited time range.
</p>
<pre>
process(
[&amp;](int, int64_t, std::complex&lt;float&gt; &amp;coef) {
coef = -coef;
},
INT_MIN, INT_MAX,
t_in - (int)analysis_support,
t_in - (int)analysis_support + (int)blocksize,
coefs);
</pre>
<p>Next, we will generate a block of output samples. To get correct results,
we can only generate output when the coefficients that the output samples
depend on will no longer change. Specifically, a resynthesized audio
sample for time <code>t</code> will depend on the coefficients of the
time range <code>t - synthesis_support</code>...<code>t +
synthesis_support</code>. To ensure that the resynthesis uses only
coefficients that have already been processed by
the <code>process()</code> call above, the most recent block of samples
that can safely be resynthesized ranges from <code>t_out = t_in -
analysis_support - synthesis_support</code> to <code>t_out +
blocksize</code>.</p>
<pre>
int64_t t_out = t_in - analysis_support - synthesis_support;
analyzer.synthesize(coefs, t_out, t_out + blocksize, buf.data());
</pre>
<p>The synthesized audio can now be written to the output file:</p>
<pre>
sf_count_t n_written = sf_writef_float(sf_out, buf.data(), blocksize);
if (n_written != blocksize) {
std::cerr &lt;&lt; "write error\n";
exit(1);
}
</pre>
<p>Coefficients older than <code>t_out + blocksize - synthesis_support</code>
will no longer be needed to synthesize the next block of output signal, so
it's now OK to forget them and free the memory they used:
</p>
<pre>
forget_before(analyzer, coefs, t_out + blocksize - synthesis_support);
</pre>
<p>This concludes the block-by-block processing loop.</p>
<pre>
t_in += blocksize;
}
</pre>
<h2>Postamble</h2>
<pre>
sf_close(sf_in);
sf_close(sf_out);
return 0;
}
</pre>
<h2>Compiling</h2>
<p>Like the previous ones, this example can also be built using a one-line build command:
</p>
<pre class="build Darwin Linux NetBSD FreeBSD">
c++ -std=c++11 -I.. -O3 -ffast-math `pkg-config --cflags sndfile` stream.cc `pkg-config --libs sndfile` -o stream
</pre>
<p>Or using the vDSP FFT on macOS:</p>
<pre class="build Darwin">
c++ -std=c++11 -I.. -O3 -ffast-math -DGABORATOR_USE_VDSP `pkg-config --cflags sndfile` stream.cc `pkg-config --libs sndfile` -framework Accelerate -o stream
</pre>
<p>Or using PFFFT (see <a href="render.html#compiling">Example 1</a> for how to download and build PFFFT):</p>
<pre class="build">
c++ -std=c++11 -I.. -Ipffft -O3 -ffast-math -DGABORATOR_USE_PFFFT `pkg-config --cflags sndfile` stream.cc pffft/pffft.o pffft/fftpack.o `pkg-config --libs sndfile` -o stream
</pre>
<h2>Running</h2>
<p>Running the following shell commands will download an example
audio file containing an impulse (a single sample of maximum amplitude)
padded with silence to a total of 65536 samples, and process it.</p>
<pre class="run">
wget http://download.gaborator.com/audio/impulse.wav
./stream impulse.wav impulse_streamed.wav
</pre>
<p>The file <code>impulse_streamed.wav</code> will be identical to
<code>impulse.wav</code> except that the impulse will be of
opposite polarity, and delayed by the latency of
<code>analysis_support + synthesis_support</code> samples.</p>
<div class="nav"><span class="prev"><a href="filter.html">Previous: Example 2: Frequency-Domain Filtering</a></span><span class="next"><a href="snr.html">Next: Example 4: Measuring the Signal-to-Noise Ratio</a></span></div>
</body>
</html>

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<!DOCTYPE html>
<!--
Copyright (C) 2020 Andreas Gustafsson. This file is part of
the Gaborator library source distribution. See the file LICENSE at
the top level of the distribution for license information.
-->
<html>
<head>
<link rel="stylesheet" href="doc.css" />
<title>Gaborator Example 5: Synthesis from Scratch</title>
</head>
<body>
<h1>Example 5: Synthesis from Scratch</h1>
<h2>Introduction</h2>
<p>This example demonstrates how to synthesize a signal by creating
spectrogram coefficients from scratch rather than by analyzing an
existing signal. It creates a random pentatonic melody of decaying
sine waves as spectrogram coefficients and then synthesizes audio
from them.
</p>
<h2>Preamble</h2>
<p>This example program takes a single command line argument, the name
of the output file.</p>
<pre>
#include &lt;memory.h&gt;
#include &lt;iostream&gt;
#include &lt;sndfile.h&gt;
#include &lt;gaborator/gaborator.h&gt;
int main(int argc, char **argv) {
if (argc &lt; 2) {
std::cerr &lt;&lt; "usage: synth output.wav\n";
exit(1);
}
</pre>
<h2>Synthesis Parameters</h2>
<p>Although this example does not perform any analysis, we nonetheless
need to create an <code>analyzer</code> object, as it is used for both
analysis and synthesis purposes. To generate the frequencies of the
12-note equal-tempered scale, we need 12 bands per octave; a multiple
of 12 would also work, but here we don't need the added frequency
resolution that would bring, and the time resolution would be
worse.</p>
<p>To simplify converting MIDI note numbers to band numbers, we choose
the frequency of MIDI note 0 as the reference frequency; this is
8.18&nbsp;Hz, which happens to be outside the frequency range of the
bandpass filter bank, but that doesn't matter.</p>
<pre>
double fs = 44100;
gaborator::parameters params(12, 20.0 / fs, 8.18 / fs);
gaborator::analyzer&lt;float&gt; analyzer(params);
</pre>
<h2>Melody Parameters</h2>
<p>
We will use the A minor pentatonic scale, which contains the
following notes (using the MIDI note numbering):</p>
<pre>
static int pentatonic[] = { 57, 60, 62, 64, 67 };
</pre>
<p>
The melody will consist of 64 notes, at a tempo of 120 beats per
minute:
</p>
<pre>
int n_notes = 64;
double tempo = 120.0;
double beat_duration = 60.0 / tempo;
</pre>
<p>
The variable <code>volume</code> determines the amplitude of
each note, and has been chosen such that there will be no clipping
of the final output.
</p>
<pre>
float volume = 0.2;
</pre>
<h2>Composition</h2>
<p>We start with an empty coefficient set:</p>
<pre>
gaborator::coefs&lt;float&gt; coefs(analyzer);
</pre>
<p>Each note is chosen randomly from the pentatonic scale and added
to the coefficient set by calling the function <code>fill()</code>.
The <code>fill()</code> function is similar to the <code>process()</code>
function used in previous examples, except that it can be used to
create new coefficients rather than just modifying existing ones.</p>
<p>Each note is created by calling <code>fill()</code> on a region of
the time-frequency plane that covers a single band in the frequency
dimension and the duration of the note in the time dimension. Each
coefficient within this region is set to a complex number whose
magnitude decays exponentially over time, like the amplitude of a
plucked string. The phase is arbitrarily set to zero by using an
imaginary part of zero. Since notes can overlap, the new coefficients
are added to any existing ones using the <code>+=</code> operator
rather than overwriting them.</p>
<p>Note that band numbers increase towards lower frequencies but MIDI
note numbers increase towards higher frequencies, hence the minus sign
in front of <code>midi_note</code>.
</p>
<pre>
for (int i = 0; i < n_notes; i++) {
int midi_note = pentatonic[rand() % 5];
double note_start_time = beat_duration * i;
double note_end_time = note_start_time + 3.0;
int band = analyzer.band_ref() - midi_note;
fill([&](int, int64_t t, std::complex&lt;float&gt; &amp;coef) {
float amplitude =
volume * expf(-2.0f * (float)(t / fs - note_start_time));
coef += std::complex&lt;float&gt;(amplitude, 0.0f);
},
band, band + 1,
note_start_time * fs, note_end_time * fs,
coefs);
}
</pre>
<h2>Synthesis</h2>
<p>We can now synthesize audio from the coefficients by
calling <code>synthesize()</code>. Audio will be generated
starting half a second before the first note to allow for the pre-ringing
of the synthesis filter, and ending a few seconds after the
last note to allow for its decay.
</p>
<pre>
double audio_start_time = -0.5;
double audio_end_time = beat_duration * n_notes + 5.0;
int64_t start_frame = audio_start_time * fs;
int64_t end_frame = audio_end_time * fs;
size_t n_frames = end_frame - start_frame;
std::vector&lt;float&gt; audio(n_frames);
analyzer.synthesize(coefs, start_frame, end_frame, audio.data());
</pre>
<h2>Writing the Audio</h2>
<p>Since there is no input audio file to inherit a file format from,
we need to choose a file format for the output file by filling in the
<code>sfinfo</code> structure:</p>
<pre>
SF_INFO sfinfo;
memset(&amp;sfinfo, 0, sizeof(sfinfo));
sfinfo.samplerate = fs;
sfinfo.channels = 1;
sfinfo.format = SF_FORMAT_WAV | SF_FORMAT_PCM_16;
</pre>
<p>The rest is identical to
<a href="filter.html#writing_audio_code">Example 2</a>:
</p>
<pre>
SNDFILE *sf_out = sf_open(argv[1], SFM_WRITE, &amp;sfinfo);
if (! sf_out) {
std::cerr &lt;&lt; "could not open output audio file: "
&lt;&lt; sf_strerror(sf_out) &lt;&lt; "\n";
exit(1);
}
sf_command(sf_out, SFC_SET_CLIPPING, NULL, SF_TRUE);
sf_count_t n_written = sf_writef_float(sf_out, audio.data(), n_frames);
if (n_written != n_frames) {
std::cerr &lt;&lt; "write error\n";
exit(1);
}
sf_close(sf_out);
return 0;
}
</pre>
<h2>Compiling</h2>
<p>Like <a href="render.html#compiling">Example 1</a>, this example
can be built using a one-line build command:
</p>
<pre class="build Darwin Linux NetBSD FreeBSD">
c++ -std=c++11 -I.. -O3 -ffast-math `pkg-config --cflags sndfile` synth.cc `pkg-config --libs sndfile` -o synth
</pre>
<p>Or using the vDSP FFT on macOS:</p>
<pre class="build Darwin">
c++ -std=c++11 -I.. -O3 -ffast-math -DGABORATOR_USE_VDSP `pkg-config --cflags sndfile` synth.cc `pkg-config --libs sndfile` -framework Accelerate -o synth
</pre>
<p>Or using PFFFT (see <a href="render.html">Example 1</a> for how to download and build PFFFT):</p>
<pre class="build">
c++ -std=c++11 -I.. -Ipffft -O3 -ffast-math -DGABORATOR_USE_PFFFT `pkg-config --cflags sndfile` synth.cc pffft/pffft.o pffft/fftpack.o `pkg-config --libs sndfile` -o synth
</pre>
<h2>Running</h2>
<p>The example program can be run using the command</p>
<pre class="run">
./synth melody.wav
</pre>
<p>The resulting audio will be in <code>melody.wav</code>.</p>
<div class="nav"><span class="prev"><a href="snr.html">Previous: Example 4: Measuring the Signal-to-Noise Ratio</a></span><span class="next"><a href="ref/intro.html">Next: API Introduction</a></span></div>
</body>
</html>

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// See ../doc/filter.html for commentary
#include <memory.h>
#include <iostream>
#include <sndfile.h>
#include <gaborator/gaborator.h>
int main(int argc, char **argv) {
if (argc < 3) {
std::cerr << "usage: filter input.wav output.wav\n";
exit(1);
}
SF_INFO sfinfo;
memset(&sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &sfinfo);
if (! sf_in) {
std::cerr << "could not open input audio file: "
<< sf_strerror(sf_in) << "\n";
exit(1);
}
double fs = sfinfo.samplerate;
sf_count_t n_frames = sfinfo.frames;
sf_count_t n_samples = sfinfo.frames * sfinfo.channels;
std::vector<float> audio(n_samples);
sf_count_t n_read = sf_readf_float(sf_in, audio.data(), n_frames);
if (n_read != n_frames) {
std::cerr << "read error\n";
exit(1);
}
sf_close(sf_in);
gaborator::parameters params(100, 20.0 / fs);
gaborator::analyzer<float> analyzer(params);
std::vector<float> band_gains(analyzer.bands_end());
for (int band = analyzer.bandpass_bands_begin(); band < analyzer.bandpass_bands_end(); band++) {
double f_hz = analyzer.band_ff(band) * fs;
band_gains[band] = 1.0 / sqrt(f_hz / 20.0);
}
band_gains[analyzer.band_lowpass()] = band_gains[analyzer.bandpass_bands_end() - 1];
for (sf_count_t ch = 0; ch < sfinfo.channels; ch++) {
std::vector<float> channel(n_frames);
for (sf_count_t i = 0; i < n_frames; i++)
channel[i] = audio[i * sfinfo.channels + ch];
gaborator::coefs<float> coefs(analyzer);
analyzer.analyze(channel.data(), 0, channel.size(), coefs);
process([&](int band, int64_t, std::complex<float> &coef) {
coef *= band_gains[band];
},
INT_MIN, INT_MAX,
INT64_MIN, INT64_MAX,
coefs);
analyzer.synthesize(coefs, 0, channel.size(), channel.data());
for (sf_count_t i = 0; i < n_frames; i++)
audio[i * sfinfo.channels + ch] = channel[i];
}
SNDFILE *sf_out = sf_open(argv[2], SFM_WRITE, &sfinfo);
if (! sf_out) {
std::cerr << "could not open output audio file: "
<< sf_strerror(sf_out) << "\n";
exit(1);
}
sf_command(sf_out, SFC_SET_CLIPPING, NULL, SF_TRUE);
sf_count_t n_written = sf_writef_float(sf_out, audio.data(), n_frames);
if (n_written != n_frames) {
std::cerr << "write error\n";
exit(1);
}
sf_close(sf_out);
return 0;
}

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// See ../doc/render.html for commentary
#include <memory.h>
#include <iostream>
#include <fstream>
#include <sndfile.h>
#include <gaborator/gaborator.h>
#include <gaborator/render.h>
int main(int argc, char **argv) {
if (argc < 3) {
std::cerr << "usage: render input.wav output.pgm\n";
exit(1);
}
SF_INFO sfinfo;
memset(&sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &sfinfo);
if (! sf_in) {
std::cerr << "could not open input audio file: "
<< sf_strerror(sf_in) << "\n";
exit(1);
}
double fs = sfinfo.samplerate;
sf_count_t n_frames = sfinfo.frames;
sf_count_t n_samples = sfinfo.frames * sfinfo.channels;
std::vector<float> audio(n_samples);
sf_count_t n_read = sf_readf_float(sf_in, audio.data(), n_frames);
if (n_read != n_frames) {
std::cerr << "read error\n";
exit(1);
}
sf_close(sf_in);
std::vector<float> mono(n_frames);
for (size_t i = 0; i < (size_t)n_frames; i++) {
float v = 0;
for (size_t c = 0; c < (size_t)sfinfo.channels; c++)
v += audio[i * sfinfo.channels + c];
mono[i] = v;
}
gaborator::parameters params(48, 20.0 / fs, 440.0 / fs);
gaborator::analyzer<float> analyzer(params);
gaborator::coefs<float> coefs(analyzer);
analyzer.analyze(mono.data(), 0, mono.size(), coefs);
int64_t x_origin = 0;
int64_t y_origin = analyzer.bandpass_bands_begin();
int x_scale_exp = 10;
while ((n_frames >> x_scale_exp) > 1000)
x_scale_exp++;
int y_scale_exp = 0;
int64_t x0 = 0;
int64_t y0 = 0;
int64_t x1 = n_frames >> x_scale_exp;
int64_t y1 = (analyzer.bandpass_bands_end() - analyzer.bandpass_bands_begin()) >> y_scale_exp;
std::vector<float> amplitudes((x1 - x0) * (y1 - y0));
gaborator::render_p2scale(
analyzer,
coefs,
x_origin, y_origin,
x0, x1, x_scale_exp,
y0, y1, y_scale_exp,
amplitudes.data());
float gain = 15;
std::ofstream f;
f.open(argv[2], std::ios::out | std::ios::binary);
f << "P5\n" << (x1 - x0) << ' ' << (y1 - y0) << "\n255\n";
for (size_t i = 0; i < amplitudes.size(); i++)
f.put(gaborator::float2pixel_8bit(amplitudes[i] * gain));
f.close();
return 0;
}

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// See ../doc/snr.html for commentary
#include <iostream>
#include <iomanip>
#include <random>
#include <gaborator/gaborator.h>
double rms(const std::vector<float> &v) {
double sqsum = 0;
for (size_t i = 0; i < v.size(); i++) {
sqsum += v[i] * v[i];
}
return sqrt(sqsum);
}
int main(int argc, char **argv) {
size_t len = 1000000;
std::vector<float> signal_in(len);
std::minstd_rand rand;
std::uniform_real_distribution<> uniform(-1.0, 1.0);
for (size_t i = 0; i < len; i++)
signal_in[i] = uniform(rand);
gaborator::parameters params(48, 5e-4);
gaborator::analyzer<float> analyzer(params);
gaborator::coefs<float> coefs(analyzer);
analyzer.analyze(signal_in.data(), 0, len, coefs);
std::vector<float> signal_out(len);
analyzer.synthesize(coefs, 0, len, signal_out.data());
std::vector<float> error(len);
for (size_t i = 0; i < len; i++)
error[i] = signal_out[i] - signal_in[i];
double snr = rms(signal_in) / rms(error);
std::cout << std::fixed << std::setprecision(1) << 20 * log10(snr) << " dB\n";
}

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// See ../doc/stream.html for commentary
#include <memory.h>
#include <iostream>
#include <sndfile.h>
#include <gaborator/gaborator.h>
int main(int argc, char **argv) {
if (argc < 3) {
std::cerr << "usage: stream input.wav output.wav\n";
exit(1);
}
SF_INFO sfinfo;
memset(&sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &sfinfo);
if (! sf_in) {
std::cerr << "could not open input audio file: "
<< sf_strerror(sf_in) << "\n";
exit(1);
}
if (sfinfo.channels != 1) {
std::cerr << "only mono files are supported\n";
exit(1);
}
double fs = sfinfo.samplerate;
SNDFILE *sf_out = sf_open(argv[2], SFM_WRITE, &sfinfo);
if (! sf_out) {
std::cerr << "could not open output audio file: "
<< sf_strerror(sf_out) << "\n";
exit(1);
}
sf_command(sf_in, SFC_SET_NORM_FLOAT, NULL, SF_FALSE);
sf_command(sf_out, SFC_SET_NORM_FLOAT, NULL, SF_FALSE);
gaborator::parameters params(12, 200.0 / fs, 440.0 / fs);
gaborator::analyzer<float> analyzer(params);
size_t analysis_support = ceil(analyzer.analysis_support());
size_t synthesis_support = ceil(analyzer.synthesis_support());
std::cerr << "latency: " << analysis_support + synthesis_support << " samples\n";
gaborator::coefs<float> coefs(analyzer);
const size_t blocksize = 1024;
std::vector<float> buf(blocksize);
int64_t t_in = 0;
for (;;) {
sf_count_t n_read = sf_readf_float(sf_in, buf.data(), blocksize);
if (n_read == 0)
break;
if (n_read < blocksize)
std::fill(buf.data() + n_read, buf.data() + blocksize, 0);
analyzer.analyze(buf.data(), t_in, t_in + blocksize, coefs);
process(
[&](int, int64_t, std::complex<float> &coef) {
coef = -coef;
},
INT_MIN, INT_MAX,
t_in - (int)analysis_support,
t_in - (int)analysis_support + (int)blocksize,
coefs);
int64_t t_out = t_in - analysis_support - synthesis_support;
analyzer.synthesize(coefs, t_out, t_out + blocksize, buf.data());
sf_count_t n_written = sf_writef_float(sf_out, buf.data(), blocksize);
if (n_written != blocksize) {
std::cerr << "write error\n";
exit(1);
}
forget_before(analyzer, coefs, t_out + blocksize - synthesis_support);
t_in += blocksize;
}
sf_close(sf_in);
sf_close(sf_out);
return 0;
}

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// See ../doc/synth.html for commentary
#include <memory.h>
#include <iostream>
#include <sndfile.h>
#include <gaborator/gaborator.h>
int main(int argc, char **argv) {
if (argc < 2) {
std::cerr << "usage: synth output.wav\n";
exit(1);
}
double fs = 44100;
gaborator::parameters params(12, 20.0 / fs, 8.18 / fs);
gaborator::analyzer<float> analyzer(params);
static int pentatonic[] = { 57, 60, 62, 64, 67 };
int n_notes = 64;
double tempo = 120.0;
double beat_duration = 60.0 / tempo;
float volume = 0.2;
gaborator::coefs<float> coefs(analyzer);
for (int i = 0; i < n_notes; i++) {
int midi_note = pentatonic[rand() % 5];
double note_start_time = beat_duration * i;
double note_end_time = note_start_time + 3.0;
int band = analyzer.band_ref() - midi_note;
fill([&](int, int64_t t, std::complex<float> &coef) {
float amplitude =
volume * expf(-2.0f * (float)(t / fs - note_start_time));
coef += std::complex<float>(amplitude, 0.0f);
},
band, band + 1,
note_start_time * fs, note_end_time * fs,
coefs);
}
double audio_start_time = -0.5;
double audio_end_time = beat_duration * n_notes + 5.0;
int64_t start_frame = audio_start_time * fs;
int64_t end_frame = audio_end_time * fs;
size_t n_frames = end_frame - start_frame;
std::vector<float> audio(n_frames);
analyzer.synthesize(coefs, start_frame, end_frame, audio.data());
SF_INFO sfinfo;
memset(&sfinfo, 0, sizeof(sfinfo));
sfinfo.samplerate = fs;
sfinfo.channels = 1;
sfinfo.format = SF_FORMAT_WAV | SF_FORMAT_PCM_16;
SNDFILE *sf_out = sf_open(argv[1], SFM_WRITE, &sfinfo);
if (! sf_out) {
std::cerr << "could not open output audio file: "
<< sf_strerror(sf_out) << "\n";
exit(1);
}
sf_command(sf_out, SFC_SET_CLIPPING, NULL, SF_TRUE);
sf_count_t n_written = sf_writef_float(sf_out, audio.data(), n_frames);
if (n_written != n_frames) {
std::cerr << "write error\n";
exit(1);
}
sf_close(sf_out);
return 0;
}

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//
// A class for affine transforms (ax + b) of scalar values
//
// Copyright (C) 2020-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_AFFINE_TRANSFORM_H
#define _GABORATOR_AFFINE_TRANSFORM_H
namespace gaborator {
struct affine_transform {
affine_transform(): a(0), b(0) { }
affine_transform(double a_, double b_): a(a_), b(b_) { }
affine_transform(const affine_transform &rhs): a(rhs.a), b(rhs.b) { }
double operator()(double x) const { return a * x + b; }
affine_transform inverse() const {
return affine_transform(1.0 / a, -b / a);
}
static affine_transform identity() { return affine_transform(1, 0); }
double a, b;
};
// Composition
static inline affine_transform
operator *(const affine_transform &a, const affine_transform &b) {
return affine_transform(a.a * b.a, a.a * b.b + a.b);
}
// Equality
static inline bool
operator ==(const affine_transform &a, const affine_transform &b) {
return a.a == b.a && a.b == b.b;
}
} // namespace
#endif

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//
// Fast Fourier transform
//
// Copyright (C) 2016-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_FFT_H
#define _GABORATOR_FFT_H
#include "gaborator/fft_naive.h"
#if GABORATOR_USE_VDSP
#include "gaborator/fft_vdsp.h"
#define GABORATOR_USE_REAL_FFT 1
#define GABORATOR_MIN_FFT_SIZE 1
#elif GABORATOR_USE_PFFFT
#include "gaborator/fft_pffft.h"
#define GABORATOR_USE_REAL_FFT 1
#define GABORATOR_MIN_FFT_SIZE 32
#else
// Use the naive FFT
// Do not define GABORATOR_USE_REAL_FFT as it is slower than
// using the complex code.
#define GABORATOR_MIN_FFT_SIZE 1
#endif
#endif

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//
// Fast Fourier transform, naive reference implementations
//
// Copyright (C) 1992-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
// Based on the module "fft" used in audsl/test, audsl/mls,
// scope/core, whitesig
#ifndef _GABORATOR_FFT_NAIVE_H
#define _GABORATOR_FFT_NAIVE_H
#include <algorithm>
#include <complex>
#include <iterator>
#include <vector>
#include <memory.h>
namespace gaborator {
template <class I>
struct fft {
typedef typename std::iterator_traits<I>::value_type C; // complex
typedef typename C::value_type T; // float/double
typedef typename std::vector<C> twiddle_vector;
fft(unsigned int n): n_(n), wtab(n / 2) { init_wtab(); }
~fft() { }
unsigned int size() { return n_; }
// Transform the contents of the array "a", leaving results in
// bit-reversed order.
void
br_transform(I a) {
unsigned int i, j, m, n;
typename twiddle_vector::iterator wp; // twiddle factor pointer
I p, q;
// n is the number of points in each subtransform (butterfly group)
// m is the number of subtransforms (butterfly groups), = n_ / n
// i is the index of the first point in the current butterfly group
// j is the number of the butterfly within the group
for (n = 2, m = n_ / 2; n <= n_; n *= 2 , m /= 2) // each stage
for (i = 0; i < n_; i += n) // each butterfly group
for (j = 0, wp = wtab.begin(), p = a + i, q = a + i + n / 2;
j < n / 2;
j++, wp += m, p++, q++) // each butterfly
{
C temp((*q) * (*wp));
*q = *p - temp;
*p += temp;
}
}
void
bit_reverse(I a) {
unsigned int i, j;
for (i = 0, j = 0; i < n_; i++, j = bitrev_inc(j)) {
if (i < j)
std::swap(*(a + i), *(a + j));
}
}
void
reverse(I a) {
for (unsigned int i = 1; i < n_ / 2; i++)
std::swap(*(a + i), *(a + n_ - i));
}
// in-place
void
transform(I a) {
bit_reverse(a);
br_transform(a);
}
void
itransform(I a) {
reverse(a);
transform(a);
}
// out-of-place
// XXX const
void
transform(I in, I out) {
std::copy(in, in + n_, out);
transform(out);
}
void
itransform(I in, I out) {
std::copy(in, in + n_, out);
itransform(out);
}
private:
// Initialize twiddle factor array
void init_wtab() {
size_t wt_size = wtab.size();
for (size_t i = 0; i < wt_size; ++i) {
double arg = (-2.0 * M_PI / n_) * i;
wtab[i] = C(cos(arg), sin(arg));
}
}
unsigned int
bitrev_inc(unsigned int i) {
unsigned int carry = n_;
do {
carry >>= 1;
unsigned int new_i = i ^ carry;
carry &= i;
i = new_i;
} while(carry);
return i;
}
// Size of the transform
unsigned int n_;
// Twiddle factor array (size n / 2)
twiddle_vector wtab;
};
// Real FFT
//
// This is a trivial implementation offering no performance advantage
// over a complex FFT. It is intended as a placeholder to be
// overridden with a specialization, and as a reference implementation
// to compare the results of specializations against.
//
template <class CI>
struct rfft {
typedef typename std::iterator_traits<CI>::value_type C; // complex
typedef typename C::value_type T; // float/double
typedef T *RI; // Real iterator
typedef const T *CONST_RI;
rfft(unsigned int n): cf(n) { }
~rfft() { }
void
transform(CONST_RI in, CI out) {
size_t n = cf.size();
C *tmp = new C[n];
C *out_tmp = new C[n];
std::copy(in, in + cf.size(), tmp); // Real to complex
cf.transform(tmp, out_tmp);
delete [] tmp;
#if GABORATOR_REAL_FFT_NEGATIVE_FQS
std::copy(out_tmp, out_tmp + n, out);
#else
std::copy(out_tmp, out_tmp + n / 2 + 1, out);
#endif
delete [] out_tmp;
}
void
itransform(CI in, RI out) {
size_t n = cf.size();
// Make sure not to use the negative frequency part of "in",
// because it may not be valid.
C *in_tmp = new C[n];
for (size_t i = 0; i < n / 2 + 1; i++) {
in_tmp[i] = in[i];
}
for (size_t i = 1; i < n / 2; i++) {
in_tmp[n - i] = conj(in[i]);
}
C *tmp = new C[n];
cf.itransform(in_tmp, tmp);
for (size_t i = 0; i < n; i++) {
*out++ = tmp[i].real();
}
delete [] tmp;
delete [] in_tmp;
}
fft<CI> cf;
};
} // Namespace
#endif

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//
// Fast Fourier transform using PFFFT
//
// Copyright (C) 2017-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_FFT_PFFFT_H
#define _GABORATOR_FFT_PFFFT_H
#include <assert.h>
#include <complex>
#include <iterator>
#include <vector>
#include "pffft.h"
// XXX disable in production
#ifdef __x86_64__
#define GABORATOR_PFFFT_CHECK_ALIGN(p) assert((((uint64_t)(p)) & 0xF) == 0)
#else
#define GABORATOR_PFFFT_CHECK_ALIGN(p) do {} while (0)
#endif
namespace gaborator {
template <>
struct fft<std::complex<float> *> {
typedef std::complex<float> *I;
typedef const std::complex<float> *CONST_I;
typedef std::iterator_traits<I>::value_type C; // complex
typedef C::value_type T; // float/double
fft(unsigned int n_): n(n_) {
setup = pffft_new_setup(n, PFFFT_COMPLEX);
assert(setup);
}
~fft() {
pffft_destroy_setup(setup);
}
unsigned int size() { return n; }
// in-place
void
transform(I a) {
pffft_transform_ordered(setup, (float *)a, (float *)a, NULL, PFFFT_FORWARD);
}
void
itransform(I a) {
pffft_transform_ordered(setup, (float *)a, (float *)a, NULL, PFFFT_BACKWARD);
}
// out-of-place
void
transform(CONST_I in, I out) {
GABORATOR_PFFFT_CHECK_ALIGN(in);
GABORATOR_PFFFT_CHECK_ALIGN(out);
pffft_transform_ordered(setup, (const float *)in, (float *)out, NULL, PFFFT_FORWARD);
}
void
itransform(CONST_I in, I out) {
GABORATOR_PFFFT_CHECK_ALIGN(in);
GABORATOR_PFFFT_CHECK_ALIGN(out);
pffft_transform_ordered(setup, (const float *)in, (float *)out, NULL, PFFFT_BACKWARD);
}
private:
// Size of the transform
unsigned int n;
PFFFT_Setup *setup;
};
// Support transforming std::vector<std::complex<float>>::iterator
template <>
struct fft<std::vector<std::complex<float>>::iterator>:
public fft<std::complex<float> *>
{
typedef fft<std::complex<float> *> base;
typedef std::vector<std::complex<float>>::iterator I;
fft(unsigned int n_): fft<std::complex<float> *>(n_) { }
void
transform(I a) {
base::transform(&(*a));
}
void
itransform(I a) {
base::itransform(&(*a));
}
void
transform(I in, I out) {
base::transform(&(*in), &(*out));
}
void
itransform(I in, I out) {
base::itransform(&(*in), &(*out));
}
};
// Use fftpack for double precision
#define FFTPACK_DOUBLE_PRECISION 1
#include "fftpack.h"
#undef FFTPACK_DOUBLE_PRECISION
template <>
struct fft<std::complex<double> *> {
typedef std::complex<double> *I;
typedef const std::complex<double> *CONST_I;
typedef std::iterator_traits<I>::value_type C; // complex
typedef C::value_type T; // float/double
fft(unsigned int n_): n(n_), wsave(4 * n_ + 15) {
cffti(n, wsave.data());
}
~fft() {
}
unsigned int size() { return n; }
// in-place
void
transform(I a) {
cfftf(n, (double *)a, wsave.data());
}
void
itransform(I a) {
cfftb(n, (double *)a, wsave.data());
}
// out-of-place
void
transform(CONST_I in, I out) {
std::copy(in, in + n, out);
transform(out);
}
void
itransform(CONST_I in, I out) {
std::copy(in, in + n, out);
itransform(out);
}
private:
// Size of the transform
unsigned int n;
std::vector<double> wsave;
};
// Real FFT
template <>
struct rfft<std::complex<float> *> {
typedef std::complex<float> *CI; // Complex iterator
typedef const std::complex<float> *CONST_CI;
typedef typename std::iterator_traits<CI>::value_type C; // complex
typedef typename C::value_type T; // float/double
typedef T *RI; // Real iterator
typedef const T *CONST_RI;
rfft(unsigned int n_): n(n_) {
setup = pffft_new_setup(n, PFFFT_REAL);
assert(setup);
}
~rfft() {
pffft_destroy_setup(setup);
}
unsigned int size() { return n; }
// out-of-place only
void
transform(CONST_RI in, CI out) {
GABORATOR_PFFFT_CHECK_ALIGN(in);
GABORATOR_PFFFT_CHECK_ALIGN(out);
pffft_transform_ordered(setup, in, (float *) out, NULL, PFFFT_FORWARD);
C tmp = out[0];
#if GABORATOR_REAL_FFT_NEGATIVE_FQS
for (unsigned int i = 1; i < (n >> 1); i++)
out[n - i] = conj(out[i]);
#endif
out[0] = C(tmp.real(), 0);
out[n >> 1] = C(tmp.imag(), 0);
}
// Note: this temporarily modifies in[0], in spite of the const
void
itransform(CONST_CI in, RI out) {
GABORATOR_PFFFT_CHECK_ALIGN(in);
GABORATOR_PFFFT_CHECK_ALIGN(out);
C tmp = in[0];
const_cast<CI>(in)[0] = C(tmp.real(), in[n >> 1].real());
pffft_transform_ordered(setup, (const float *) in, out, NULL, PFFFT_BACKWARD);
const_cast<CI>(in)[0] = tmp;
}
private:
// Size of the transform
unsigned int n;
PFFFT_Setup *setup;
};
#undef GABORATOR_PFFFT_CHECK_ALIGN
} // namespace
#endif

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//
// Fast Fourier transform using the Apple vDSP framework
//
// Copyright (C) 2013-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_FFT_VDSP_H
#define _GABORATOR_FFT_VDSP_H
#include <assert.h>
#include <iterator>
#include <vector>
#include <memory.h>
#include <mach/mach.h>
#include <mach/task.h>
#include <mach/task_info.h>
#include <mach/vm_map.h>
#include <Accelerate/Accelerate.h>
namespace gaborator {
static inline int log2_int_exact(int n) {
// n must be a power of two
assert(n != 0 && ((n & (n >> 1)) == 0));
int r = 0;
for (;;) {
n >>= 1;
if (n == 0)
break;
r++;
}
return r;
}
template <>
struct fft<std::complex<float> *> {
typedef std::complex<float> *I;
typedef typename std::iterator_traits<I>::value_type C; // complex
typedef typename C::value_type T; // float/double
fft(unsigned int n_): n(n_), log2n(log2_int_exact(n)) {
setup = vDSP_create_fftsetup(log2n, kFFTRadix2);
}
~fft() {
vDSP_destroy_fftsetup(setup);
}
unsigned int size() { return n; }
// in-place
void
transform(I a) {
DSPSplitComplex s;
// XXX this result in disoptimal alignment
s.realp = (float *) a;
s.imagp = (float *) a + 1;
vDSP_fft_zip(setup, &s, 2, log2n, kFFTDirection_Forward);
}
void
itransform(I a) {
DSPSplitComplex s;
s.realp = (float *) a;
s.imagp = (float *) a + 1;
vDSP_fft_zip(setup, &s, 2, log2n, kFFTDirection_Inverse);
}
// out-of-place
// XXX const
void
transform(I in, I out) {
DSPSplitComplex si;
si.realp = (float *) in;
si.imagp = (float *) in + 1;
DSPSplitComplex so;
so.realp = (float *) out;
so.imagp = (float *) out + 1;
vDSP_fft_zop(setup,
&si, 2,
&so, 2,
log2n, kFFTDirection_Forward);
}
void
itransform(I in, I out) {
DSPSplitComplex si;
si.realp = (float *) in;
si.imagp = (float *) in + 1;
DSPSplitComplex so;
so.realp = (float *) out;
so.imagp = (float *) out + 1;
vDSP_fft_zop(setup,
&si, 2,
&so, 2,
log2n, kFFTDirection_Inverse);
}
private:
// Size of the transform
unsigned int n;
unsigned int log2n;
FFTSetup setup;
};
// Real FFT
template <>
struct rfft<std::complex<float> *> {
typedef std::complex<float> *CI; // Complex iterator
typedef const std::complex<float> *CONST_CI;
typedef typename std::iterator_traits<CI>::value_type C; // complex
typedef typename C::value_type T; // float/double
typedef T *RI; // Real iterator
typedef const T *CONST_RI;
rfft(unsigned int n_): n(n_), log2n(log2_int_exact(n)) {
setup = vDSP_create_fftsetup(log2n, kFFTRadix2);
}
~rfft() {
vDSP_destroy_fftsetup(setup);
}
unsigned int size() { return n; }
// out-of-place only
void
transform(CONST_RI in, CI out) {
DSPSplitComplex si;
si.realp = (float *) in;
si.imagp = (float *) in + 1;
DSPSplitComplex so;
so.realp = (float *) out;
so.imagp = (float *) out + 1;
vDSP_fft_zrop(setup,
&si, 2,
&so, 2,
log2n, kFFTDirection_Forward);
// Undo vDSP scaling
for (unsigned int i = 0; i < (n >> 1); i++)
out[i] *= (T)0.5;
C tmp = out[0];
#if GABORATOR_REAL_FFT_NEGATIVE_FQS
for (unsigned int i = 1; i < (n >> 1); i++)
out[n - i] = conj(out[i]);
#endif
out[0] = C(tmp.real(), 0);
out[n >> 1] = C(tmp.imag(), 0);
}
void
itransform(CONST_CI in, RI out) {
C tmp = in[0];
const_cast<CI>(in)[0] = C(tmp.real(), in[n >> 1].real());
DSPSplitComplex si;
si.realp = (float *) in;
si.imagp = (float *) in + 1;
DSPSplitComplex so;
so.realp = (float *) out;
so.imagp = (float *) out + 1;
vDSP_fft_zrop(setup,
&si, 2,
&so, 2,
log2n, kFFTDirection_Inverse);
const_cast<CI>(in)[0] = tmp;
}
private:
// Size of the transform
unsigned int n;
unsigned int log2n;
FFTSetup setup;
};
// Support transforming std::vector<std::complex<float>>::iterator
template <>
struct fft<typename std::vector<std::complex<float>>::iterator>:
public fft<std::complex<float> *>
{
typedef fft<std::complex<float> *> base;
typedef typename std::vector<std::complex<float>>::iterator I;
fft(unsigned int n_): fft<std::complex<float> *>(n_) { }
void
transform(I a) {
base::transform(&(*a));
}
void
itransform(I a) {
base::itransform(&(*a));
}
void
transform(I in, I out) {
base::transform(&(*in), &(*out));
}
void
itransform(I in, I out) {
base::itransform(&(*in), &(*out));
}
};
} // Namespace
#endif

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//
// The Gaussian and related functions
//
// Copyright (C) 2015-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_GAUSSIAN_H
#define _GABORATOR_GAUSSIAN_H
#include <math.h>
namespace gaborator {
// A rough approximation of erfc_inv(), the inverse complementary
// error function. This is good for arguments in the range 1e-8 to 1,
// to within a few percent.
inline float erfc_inv(float x) {
return sqrtf(-logf(x)) - 0.3f;
}
// Gaussian with peak = 1
inline double norm_gaussian(double sd, double x) {
return exp(-(x * x) / (2 * sd * sd));
}
// Gaussian with integral = 1
inline double gaussian(double sd, double x) {
double a = 1.0 / (sd * sqrt(2.0 * M_PI));
return a * norm_gaussian(sd, x);
}
// The convolution of a Heaviside step function with a Gaussian of
// standard deviation sd. Goes smoothly from 0 to 1, with the 0.5
// point at x=0.
static inline
double gaussian_edge(double sd, double x) {
double erf_arg = x / (sd * M_SQRT2);
if (erf_arg < -7)
return 0; // error < 5e-23
if (erf_arg > 7)
return 1; // error < 5e-23
return (erf(erf_arg) + 1) * 0.5;
}
// Translate the time-domain standard deviation of a Gaussian
// (in samples) into the corresponding frequency-domain standard
// deviation (as a fractional frequency), or vice versa.
static inline double sd_t2f(double st_sd) {
return 1.0 / (2.0 * M_PI * st_sd);
}
static inline double sd_f2t(double ff_sd) {
return sd_t2f(ff_sd);
}
// Given a Gaussian with standard deviation "sd" and a maximum error
// "max_error", calculate the support needed on each side to keep the
// area below the curve within max_error of the exact value.
static inline
double gaussian_area_support(double sd, double max_error) {
return sd * M_SQRT2 * erfc_inv(max_error);
}
// Inverse of the above: given a support and maximum error, calculate
// the standard deviation.
static inline
double gaussian_area_support_inv(double support, double max_error) {
return support / (M_SQRT2 * erfc_inv(max_error));
}
// Given a gaussian with standard deviation "sd" and a maximum error
// "max_error", calculate the support needed on each side for the
// value to fall to a factor of "max_error" of the peak.
static inline
double gaussian_value_support(double sd, double max_error) {
return sd * M_SQRT2 * sqrt(-log(max_error));
}
// Inverse of the above: given a support and maximum error, calculate
// the standard deviation.
static inline
double gaussian_value_support_inv(double support, double max_error) {
return support / (M_SQRT2 * sqrt(-log(max_error)));
}
// Choose which criterion to use
#if 1
static inline
double gaussian_support(double support, double max_error) {
return gaussian_area_support(support, max_error);
};
static inline
double gaussian_support_inv(double support, double max_error) {
return gaussian_area_support_inv(support, max_error);
};
#else
static inline
double gaussian_support(double support, double max_error) {
return gaussian_value_support(support, max_error);
};
static inline
double gaussian_support_inv(double support, double max_error) {
return gaussian_value_support_inv(support, max_error);
};
#endif
} // namespace
#endif

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//
// A vector class without default-initialization, for "plain old data"
//
// Copyright (C) 2016-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_POD_VECTOR_H
#define _GABORATOR_POD_VECTOR_H
#include <stdlib.h> // size_t
#include <algorithm> // std::swap
namespace gaborator {
// A vector for storing Plain Old Data. This is similar to a
// std::vector, except that it does not zero-initialize elements,
// and that it guarantees that data() returns a non-NULL pointer
// even when the vector contains zero elements.
template <class T>
struct pod_vector {
typedef T value_type;
typedef T *iterator;
pod_vector() {
b = e = 0;
}
explicit pod_vector(size_t size_) {
// Allocate raw uninitialized memory
b = static_cast<T *>(::operator new(size_ * sizeof(T)));
e = b + size_;
}
~pod_vector()
#if __cplusplus >= 201103L
noexcept
#endif
{
_free();
}
void swap(pod_vector &x) {
std::swap(b, x.b);
std::swap(e, x.e);
}
iterator begin() const { return b; }
iterator end() const { return e; }
T *data() { return b; }
const T *data() const { return b; }
T &operator[](size_t i) { return b[i]; }
const T &operator[](size_t i) const { return b[i]; }
size_t size() const { return e - b; }
void resize(size_t new_size) {
if (new_size == size())
return;
T *n = static_cast<T *>(::operator new(new_size * sizeof(T)));
size_t ncopy = std::min(size(), new_size);
std::copy(b, b + ncopy, n);
_free();
b = n;
e = n + new_size;
}
pod_vector(const pod_vector &a)
{
b = new T[a.size()];
e = b + a.size();
std::copy(a.b, a.e, b);
//if (size()) fprintf(stderr, "pod_vector cc %d\n", (int)size());
}
void clear() {
_free();
b = e = 0;
}
#if __cplusplus >= 201103L
pod_vector(pod_vector&& x) noexcept:
b(x.b), e(x.e)
{
x.b = x.e = 0;
//if (size()) fprintf(stderr, "pod_vector mv %d\n", (int)size());
}
#endif
pod_vector &operator=(const pod_vector &a) {
if (&a == this)
return *this;
_free();
b = static_cast<T *>(::operator new(a.size() * sizeof(T)));
e = b + a.size();
std::copy(a.b, a.e, b);
//if (size()) fprintf(stderr, "pod_vector = %d\n", (int)size());
return *this;
}
#if __cplusplus >= 201103L
pod_vector &operator=(pod_vector &&x) noexcept {
if (&x == this)
return *this;
_free();
b = x.b;
e = x.e;
x.b = x.e = 0;
return *this;
}
#endif
private:
void _free() {
// Free as raw uninitialized memory
::operator delete(b);
}
private:
T *b;
T *e;
};
} // namespace
#endif

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//
// Pool of shared objects
//
// Copyright (C) 2015-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_POOL_H
#define _GABORATOR_POOL_H
#include <map>
namespace gaborator {
// The "pool" class is for sharing FFT objects so that we don't
// create multiple FFTs of the same size. It could also be used
// to share objects of some other class T where we don't want to
// create multiple Ts with the same K.
template <class T, class K>
struct pool {
typedef std::map<K, T *> m_t;
~pool() {
for (typename m_t::iterator it = m.begin(); it != m.end(); it++) {
delete (*it).second;
}
}
T *get(const K &k) {
std::pair<typename m_t::iterator, bool> r = m.insert(std::make_pair(k, (T *)0));
if (r.second) {
// New element was inserted
assert((*(r.first)).second == 0);
(*r.first).second = new T(k);
}
return (*r.first).second;
}
m_t m;
static pool shared;
};
template <class T, class K>
pool<T, K> pool<T, K>::shared;
} // namespace
#endif

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//
// Intrusive reference counting smart pointer
//
// Copyright (C) 2016-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_REF_H
#define _GABORATOR_REF_H
namespace gaborator {
template <class T> struct ref;
struct refcounted {
refcounted() { refcount = 0; }
unsigned int refcount;
};
// Template functions for manual reference counting, without using the
// ref<> class. It would be tempting to make these methods of struct
// refcounted, but that won't work because it would lose the full
// object type and invoke operator delete on the base class.
template <class T>
void incref(T &r) {
r.refcount++;
}
template <class T>
void decref(T &r) {
r.refcount--;
if (r.refcount == 0)
delete &r;
}
template <class T>
struct ref {
ref(): p(0) { }
ref(T *p_): p(p_) {
_incref();
}
ref(const ref &o): p(o.p) {
_incref();
}
ref &operator=(const ref &o) { reset(o.p); return *this; }
~ref() { reset(); }
void reset() {
_decref();
p = 0;
}
void reset(T *n) {
if (n == p)
return;
_decref();
p = n;
_incref();
}
T *get() const { return p; }
T *operator->() const { return p; }
T &operator*() const { return *p; }
operator bool() const { return p; }
private:
void _incref() {
if (! p)
return;
incref(*p);
}
void _decref() {
if (! p)
return;
decref(*p);
}
T *p;
};
} // namespace
#endif

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//
// Rendering of spectrogram images
//
// Copyright (C) 2015-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_RENDER_H
#define _GABORATOR_RENDER_H
#include "gaborator/gaborator.h"
#include "gaborator/resample2.h"
namespace gaborator {
// Convert a floating-point linear brightness value in the range 0..1
// into an 8-bit pixel value, with clamping and (rough) gamma
// correction. This nominally uses the sRGB gamma curve, but the
// current implementation cheats and uses a gamma of 2 because it can
// be calculated quickly using a square root.
template <class T>
unsigned int float2pixel_8bit(T val) {
// Clamp before gamma correction so we don't take the square root
// of a negative number; those can arise from bicubic
// interpolation. While we're at it, let's also skip the gamma
// correction for small numbers that will round to zero anyway,
// and especially denormals which could rigger GCC bug target/83240.
static const T almost_zero = 1.0 / 65536;
if (val < almost_zero)
val = 0;
if (val > 1)
val = 1;
return (unsigned int)(sqrtf(val) * 255.0f);
}
//////////////////////////////////////////////////////////////////////////////
// Power-of-two rendering
// Magnitude
template<class T>
struct complex_abs_fob {
T operator()(const complex<T> &c) {
return complex_abs(c);
}
typedef T return_type;
};
// T -> f() -> OI::value_type
template <class F, class OI, class T>
struct transform_output_iterator: public std::iterator<std::output_iterator_tag, T> {
typedef T value_type;
transform_output_iterator(F f_, OI output_): f(f_), output(output_) { }
transform_output_iterator<F, OI, T>& operator=(T v) {
*output++ = f(v);
return *this;
}
transform_output_iterator<F, OI, T>& operator*() { return *this; }
transform_output_iterator<F, OI, T>& operator++() { return *this; }
transform_output_iterator<F, OI, T>& operator++(int) { return *this; }
F f;
OI output;
};
// A source object for resample2() that provides the
// values of a row of spectrogram coordinates transformed
// by function normf (typically an absolute value function).
//
// T is the analyzer signal type
// C is the coefficient type
// OI is the output iterator type
template <class T, class C, class OI, class NORMF>
struct abs_row_source {
typedef transform_output_iterator<NORMF, OI, C> abs_writer_t;
abs_row_source(const coefs<T, C> &coefs_,
int oct_, unsigned int obno_,
NORMF normf_):
rs(coefs_, oct_, obno_),
normf(normf_)
{ }
OI operator()(sample_index_t i0, sample_index_t i1, OI output) const {
abs_writer_t abswriter(normf, output);
abs_writer_t abswriter_end = rs(i0, i1, abswriter);
return abswriter_end.output;
}
row_source<T, abs_writer_t, C> rs;
NORMF normf;
};
// Helper class for abs_row_source specialization below
template <class C, class OI>
struct abs_writer_dest {
abs_writer_dest(OI output_): output(output_) { }
void process_existing_slice(C *bv, size_t len) {
complex_magnitude(bv, output, len);
output += len;
}
void process_missing_slice(size_t len) {
for (size_t i = 0; i < len; i++)
*output++ = 0;
}
OI output;
};
// Partial specialization of class abs_row_source for NORMF = complex_abs_fob,
// for vectorization.
template <class T, class C, class OI>
struct abs_row_source<T, C, OI, struct complex_abs_fob<T>> {
// Note unused last arg
abs_row_source(const coefs<T, C> &coefs_,
int oct_, unsigned int obno_,
complex_abs_fob<T>):
slicer(coefs_, oct_, obno_)
{ }
OI operator()(coef_index_t i0, coef_index_t i1, OI output) const {
abs_writer_dest<C, OI> dest(output);
slicer(i0, i1, dest);
return dest.output;
}
row_foreach_slice<T, abs_writer_dest<C, OI>, C> slicer;
};
// Render a single line (single frequency band), with scaling in the
// horizontal (time) dimension, and filtering to avoid aliasing when
// minifying.
template <class OI, class T, class C, class NORMF, class RESAMPLER>
OI render_line(const analyzer<T> &anl,
const coefs<T, C> &msc,
int gbno,
affine_transform xf,
sample_index_t i0, sample_index_t i1,
OI output,
NORMF normf)
{
typedef typename NORMF::return_type RST;
int oct;
unsigned int obno; // Band number within octave
bool clip = ! bno_split(*msc.meta, gbno, oct, obno, false);
if (clip) {
for (sample_index_t i = i0; i < i1; i++)
*output++ = (T)0;
return output;
}
abs_row_source<T, C, RST *, NORMF>
abs_rowsource(msc, oct, obno, normf);
// Scale by the downsampling factor of the band
int scale_exp = band_scale_exp(*msc.octaves[oct].meta, oct, obno);
RESAMPLER x_resampler(zoom_p2(xf, -scale_exp));
output = x_resampler(abs_rowsource, i0, i1, output);
return output;
}
// Render a two-dimensional image with scaling in the horizontal
// direction only. In the vertical direction, there is always a
// one-to-one correspondence between bands and pixels. yi0 and yi1
// already have the yorigin applied, so there is no yorigin argument.
template <class OI, class T, class C, class NORMF, class RESAMPLER>
OI render_noyscale(const analyzer<T> &anl,
const coefs<T, C> &msc,
affine_transform x_xf,
int64_t xi0, int64_t xi1,
int64_t yi0, int64_t yi1,
OI output,
int64_t output_stride,
NORMF normf)
{
assert(xi1 >= xi0);
int w = (int)(xi1 - xi0);
assert(w >= 0);
int gbno0 = (int)yi0;
int gbno1 = (int)yi1;
for (int gbno = gbno0; gbno < gbno1; gbno++) {
render_line<OI, T, C, NORMF, RESAMPLER>
(anl, msc, gbno, x_xf,
xi0, xi1,
output, normf);
output += output_stride;
}
return output;
}
// Source data from a column of a row-major two-dimensional array.
// data points to the beginning of a row-major array with an x
// range of x0..x1 and an y range from y0..y1, and operator()
// returns data from column x (where x is within the range x0..x1).
template <class T, class OI>
struct transverse_source {
transverse_source(T *data_,
int64_t x0_, int64_t x1_, int64_t y0_, int64_t y1_,
int64_t x_):
data(data_),
x0(x0_), x1(x1_), y0(y0_), y1(y1_),
x(x_),
stride(x1 - x0)
{ }
OI operator()(int64_t i0, int64_t i1, OI out) const {
assert(x >= x0);
assert(x <= x1);
assert(i1 >= i0);
assert(i0 >= y0);
assert(i1 <= y1);
T *p = data + (x - x0) + (i0 - y0) * stride;
while (i0 != i1) {
*out++ = *p;
p += stride;
++i0;
}
return out;
}
T *data;
int64_t x0, x1, y0, y1, x;
size_t stride;
};
template <class I>
struct stride_iterator: public std::iterator
<std::forward_iterator_tag, typename std::iterator_traits<I>::value_type>
{
typedef typename std::iterator_traits<I>::value_type T;
stride_iterator(I it_, size_t stride_): it(it_), stride(stride_) { }
T& operator*() { return *it; }
stride_iterator<I>& operator++() {
it += stride;
return *this;
}
stride_iterator operator++(int) {
stride_iterator old = *this;
it += stride;
return old;
}
I it;
size_t stride;
};
struct updated_nop {
void operator()(int64_t x0, int64_t x1, int64_t y0, int64_t y1) { }
};
// Render a two-dimensional image with scaling in both the horizontal
// (time) and vertical (frequency) directions. The output may be
// written through "output" out of order, so "output" must be a random
// access iterator.
// Note the default template argument for NORMF. This is needed
// because the compiler won't deduce the type of NORMF from the
// default function argument "NORMF normf = complex_abs_fob<T>()"
// when the normf argument is omitted; it is considered a "non-deduced
// context", being "a template parameter used in the parameter type of
// a function parameter that has a default argument that is being used
// in the call for which argument deduction is being done".
// Unfortuantely, this work-around of providing a default template
// argument requires C++11.
// This supports incremental rendering where only the parts of the
// output image affected by analyzing a given time range of samples
// are updated, the time range being from inc_i0 (inclusive) to inc_i1
// (exclusive). The updated parts of the image consist of zero or
// more non-overlapping rectangles; to find out what those are, pass a
// function "update" which will be called will each rectangle in turn
// after it has been updated.
// For non-incremental rendering, pass inc_i0 = INT64_MIN and inc_i1 =
// INT64_MAX.
// OI is the output iterator type
// T is the coefficient type
template <class OI, class T, class C, class NORMF = complex_abs_fob<T>,
class RESAMPLER = lanczos2_pow2_resampler,
class UPDATEDF = updated_nop>
void render_incremental(
const analyzer<T> &anl,
const coefs<T, C> &msc,
affine_transform x_xf, affine_transform y_xf,
int64_t xi0, int64_t xi1,
int64_t yi0, int64_t yi1,
int64_t inc_i0, int64_t inc_i1,
OI output,
int64_t output_stride,
NORMF normf = complex_abs_fob<T>(),
UPDATEDF updated = updated_nop())
{
assert(xi1 >= xi0);
assert(yi1 >= yi0);
assert(inc_i1 >= inc_i0);
// The data type to reasmple
typedef typename NORMF::return_type RST;
// Vertical resampler
RESAMPLER y_resampler(y_xf);
// Find the image bounds in the spectrogram coordinate system,
// including the interpolation margin. The Y bounds are in
// bands and are used both to determine what to render into the
// temporary image and for short-circuiting. The X bounds are in
// coefficient samples, and are only used for short-circuiting.
// The X bounds will be calculated later if we need them.
int64_t ysi0, ysi1;
y_resampler.support(yi0, yi1, ysi0, ysi1);
// Calculate adjusted image X bounds based on the updated signal
// range for incremental rendering, and return an estimate of the
// numbers of pixels we can avoid rendering at this Y coordinate
// by using the adjusted X bounds.
auto savings = [&](int64_t y, int64_t &adj_x0, int64_t &adj_x1) {
// Find the highest-index / lowest-frequency band used
// as a resampler input for output pixel y; it will have
// the widest analysis support in the x direction.
// Note that we pass y twice, and ignore the ysi0 result.
int64_t ysi0, ysi1;
y_resampler.support(y, y, ysi0, ysi1);
int64_t band = ysi1;
// Clamp the band to the valid range
band = std::max(band, (int64_t)anl.bandpass_bands_begin());
band = std::min(band, (int64_t)anl.bandpass_bands_end() - 1);
// Find the analysis support in the time (x) dimension,
// in signal samples
double support = anl.analysis_support(band);
// Convert from signal samples to coefficient samples
int scale_exp = anl.band_scale_exp((int)band);
// Extend the updated coefficient range by the analysis
// support, and map it back to pixel space to find the
// affected pixel range, taking the resampler support
// into account.
RESAMPLER x_resampler(zoom_p2(x_xf, -scale_exp));
int64_t ceil_support = ceil(support);
// inv_support() calculates both sides of the support at once,
// but in the one-sided case, passing INT64_MIN/MAX may cause
// overflow and undefined behavior. Therefore, we pass a
// dummy value of zero instead, and make sure not to use the
// corresponding output value. This may cause the two inputs
// to inv_support() to be out of order, so it needs to accept
// that.
x_resampler.inv_support(
inc_i0 == INT64_MIN ? (int64_t)0 : (inc_i0 - ceil_support) >> scale_exp,
inc_i1 == INT64_MAX ? (int64_t)0 : (inc_i1 + ceil_support) >> scale_exp,
adj_x0,
adj_x1);
if (inc_i0 == INT64_MIN) {
adj_x0 = xi0;
} else {
adj_x0 = std::max(xi0, adj_x0);
// Don't let width go negative
adj_x0 = std::min(adj_x0, xi1);
}
if (inc_i1 == INT64_MAX) {
adj_x1 = xi1;
} else {
adj_x1 = std::min(xi1, adj_x1);
// Don't let width go negative
adj_x1 = std::max(adj_x1, adj_x0);
}
assert(adj_x0 <= adj_x1);
return (adj_x0 - xi0) + (xi1 - adj_x1);
};
if (!(inc_i0 == INT64_MIN && inc_i1 == INT64_MAX)) {
// Incremental rendering has been requested
int64_t adj_x0_top, adj_x1_top, adj_x0_bot, adj_x1_bot;
// See how much rendering we can save per line at the bottom,
// and calcualate adjusted bounds
int64_t bot_savings = savings(ysi1, adj_x0_bot, adj_x1_bot);
// See how much rendering we can save per line at the top
int64_t top_savings = savings(ysi0, adj_x0_top, adj_x1_top);
// Adjust bounds and output pointer to realize the bottom
// savings
if (adj_x0_bot == adj_x1_bot)
return;
output += adj_x0_bot - xi0;
xi0 = adj_x0_bot;
xi1 = adj_x1_bot;
// If the savings at the top are significantly greater than
// at the bottom, it pays to subdivde the area to render,
// so that the top part can benefit from the greater savings
// there.
if (((top_savings - bot_savings) * (yi1 - yi0)) > 1000) {
// Subdivide vertically
int64_t ysplit = (yi1 + yi0) >> 1;
size_t output_offset = (ysplit - yi0) * output_stride;
render_incremental<OI, T, C, NORMF, RESAMPLER, UPDATEDF>
(anl, msc, x_xf, y_xf,
xi0, xi1,
yi0, ysplit,
inc_i0, inc_i1,
output, output_stride, normf, updated);
render_incremental<OI, T, C, NORMF, RESAMPLER, UPDATEDF>
(anl, msc, x_xf, y_xf,
xi0, xi1,
ysplit, yi1,
inc_i0, inc_i1,
output + output_offset, output_stride, normf, updated);
return;
}
}
// Horizontal resampler, used only to calculate the support for
// short-circuiting. Since the resampling factor varies by band,
// the support also varies; use the largest resampling factor of
// any band to get the worst-case support.
int worstcase_band = anl.bandpass_bands_end() - 1;
RESAMPLER x_resampler(zoom_p2(x_xf, -anl.band_scale_exp(worstcase_band)));
int64_t xsi0, xsi1;
x_resampler.support(xi0, xi1, xsi0, xsi1);
// Short-circuiting: if the image to be rendered falls entirely
// outside the data, just set it to zero instead of resampling down
// (potentially) high-resolution zeros to the display resolution.
// This makes a difference when zooming out by a large factor, for
// example such that the entire spectrogram falls within a single
// tile; that tile will necessarily be expensive to calculate, but
// the other tiles need not be, and mustn't be if we are to keep
// the total amount of work bounded by O(L) with respect to the
// signal length L regardless of zoom.
coef_index_t cxi0, cxi1;
get_band_coef_bounds(msc, worstcase_band, cxi0, cxi1);
if (ysi1 < 0 || // Entirely above
ysi0 >= anl.n_bands_total - 1 || // Entirely below
xsi1 < cxi0 || // Entirely to the left
xsi0 >= cxi1) // Entirely to the right
{
size_t n = (size_t)((yi1 - yi0) * (xi1 - xi0));
for (size_t i = 0; i < n; i++)
output[i] = (T)0;
return;
}
if (y_xf.a == 1 && y_xf.b == 0) {
// No Y resampling needed, render data resampled in the X
// direction only.
render_noyscale<OI, T, C, NORMF, RESAMPLER>
(anl, msc, x_xf, xi0, xi1, yi0, yi1,
output, output_stride, normf);
} else {
// Construct a temporary image resampled in the
// X direction, but not yet in the Y direction. Include
// extra scanlines at the top and bottom for interpolation.
size_t n_pixels = (size_t)((ysi1 - ysi0) * (xi1 - xi0));
pod_vector<RST> render_data(n_pixels);
// Render data resampled in the X direction
RST *p = render_data.data();
render_noyscale<OI, T, C, NORMF, RESAMPLER>
(anl, msc, x_xf, xi0, xi1,
ysi0, ysi1, p, xi1 - xi0, normf);
// Resample in the Y direction
for (int64_t xi = xi0; xi < xi1; xi++) {
transverse_source<RST, OI> src(render_data.data(),
xi0, xi1, ysi0, ysi1,
xi);
stride_iterator<OI> dest(output + (xi - xi0), output_stride);
y_resampler(src, yi0, yi1, dest);
}
}
updated(xi0, xi1, yi0, yi1);
}
template <class OI, class T, class C, class NORMF = complex_abs_fob<T>,
class RESAMPLER = lanczos2_pow2_resampler>
void render_p2scale(const analyzer<T> &anl,
const coefs<T, C> &msc,
int64_t xorigin, int64_t yorigin,
int64_t xi0, int64_t xi1, int xe,
int64_t yi0, int64_t yi1, int ye,
OI output,
NORMF normf = complex_abs_fob<T>())
{
// Provide default inc_i0, inc_i1, and output_stride
render_incremental<OI, T, C, NORMF, RESAMPLER>
(anl, msc,
affine_transform(ldexp(1, xe), xorigin),
affine_transform(ldexp(1, ye), yorigin),
xi0, xi1, yi0, yi1,
INT64_MIN, INT64_MAX,
output, xi1 - xi0, normf);
}
} // namespace
#endif

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//
// Fast resampling by powers of two
//
// Copyright (C) 2016-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
// Uses a two-lobe Lanczos kernel. Good enough for image data, not
// intended for audio.
#ifndef _GABORATOR_RESAMPLE2_H
#define _GABORATOR_RESAMPLE2_H
#include <assert.h>
#include <inttypes.h>
#include <math.h>
#include <algorithm> // std::copy
#include "gaborator/affine_transform.h"
#include "gaborator/pod_vector.h"
namespace gaborator {
//
// There are two ways to look at this.
//
// In one point of view, there is only one coordinate space, and
// coordinates are floating-point numbers. The various sub- and
// supersampled views differ in step sizes and the number of
// fractional coordinate bits, but any given coordinates refer to the
// same point in the image at any scale. Steps are powers of two,
// with integer exponents that may be negative. A step size > 1
// implies downsampling (antialias lowpass filtering and subsampling),
// and a step size < 1 implies upsampling (aka interpolation).
//
// The coordinates are always integer multiples of the step size.
//
// e.g.,
// x0 = 33.5, xstep = 0.5
// x0 = 12, xstep = 4
//
// In the other point of view, we introduce an integer exponent e and
// substitute x0 = i0 * 2^e and xstep = 2^e. Now instead of floating
// point coordinates, we use integer "indices". The above example
// now looks like his:
//
// i0 = 67, e = -1
// i0 = 3, e = 2
//
// This latter point of view is how the code actually works.
//
// A power-of-two transform, as in y = 2^e x + origin
struct p2_transform {
p2_transform(int e_, int64_t origin_): e(e_), origin(origin_) { }
// Convert a linear transform into a p2_transform
p2_transform(affine_transform xf) {
int exp;
double m = frexp(xf.a, &exp);
assert(m == 0.5);
e = exp - 1;
origin = xf.b;
assert(origin == xf.b); // No fraction
}
int e;
int64_t origin;
};
// Scale a transform by a power of two
static inline p2_transform
zoom_p2(p2_transform xf, int e) {
return p2_transform(xf.e + e, xf.origin);
}
static inline affine_transform
zoom_p2(affine_transform xf, int e) {
return affine_transform(ldexp(xf.a, e), xf.b);
}
// Resample data from "source", generating a view between indices
// i0 and i1 of the scale determined by exponent e, and storing
// i1 - i0 samples starting at *out.
//
// The source must implement an operator() taking the arguments
// (int64_t i0, int64_t i1, T *out) and generating data for the base
// resolution (e=0).
//
// S is the type of the data source
// OI is the output iterator type
template <class S, class OI>
OI resample2_p2xf(const S &source, p2_transform xf,
int64_t i0, int64_t i1,
bool interpolate, OI out)
{
typedef typename std::iterator_traits<OI>::value_type T;
assert(i1 >= i0);
if (xf.e > 0) {
// Downsample
// Calculate super-octave coordinates
// margin is the support of the resampling kernel (on each side,
// not counting the center sample)
int margin = interpolate ? 1 : 0;
// When margin = 1, we use three samples, at 2i-1, 2i, 2i+1
// and the corresponding half-open inverval is 2i-1...2i+1+1
int64_t si0 = 2 * i0 - margin;
int64_t si1 = 2 * i1 + margin + 1;
// Get super-octave data
gaborator::pod_vector<T> super_data(si1 - si0);
T *p = super_data.data();
p = resample2_p2xf(source, p2_transform(xf.e - 1, xf.origin),
si0, si1, interpolate, p);
assert(p == super_data.data() + si1 - si0);
for (int64_t i = i0; i < i1; i++) {
int64_t si = 2 * i - si0;
T val;
if (!interpolate) {
// Point sampling
val = super_data[si];
} else {
// Triangular kernel
T v1 = super_data[si - 1];
T v0 = super_data[si];
v1 += super_data[si + 1];
val =
v0 * (T)0.5 +
v1 * (T)0.25;
#if 0 // Lanczos2 is overkill when downsampling.
} else {
// Two-lobe Lanczos kernel, needs margin = 2
// Always aligned
T v3 = super_data[si - 3];
// There is no v2
T v1 = super_data[si - 1];
T v0 = super_data[si];
// There is still no v2
v1 += super_data[si + 1];
v3 += super_data[si + 3];
val =
v0 * (T)0.49530706 +
v1 * (T)0.28388978 +
v3 * (T)-0.03154331;
#endif
}
*out++ = val;
}
} else if (xf.e < 0) {
// Upsample
if (! interpolate) {
// Return nearest neighbor. If the pixel lies
// exactly at the midpoint between the neighbors,
// return their average.
int sh = -xf.e;
int64_t si0 = i0 >> sh;
int64_t si1 = ((i1 - 1) >> sh) + 1 + 1;
gaborator::pod_vector<T> source_data(si1 - si0);
source(xf.origin + si0, xf.origin + si1, source_data.data());
for (int64_t i = i0; i < i1; i++) {
int64_t si = (i >> sh) - si0;
T val;
int rem = i & ((1 << sh) - 1);
int half = (1 << sh) >> 1;
if (rem < half) {
val = source_data[si];
} else if (rem == half) {
val = (source_data[si] + source_data[si + 1]) * (T)0.5;
} else { // rem > half
val = source_data[si + 1];
}
*out++ = val;
}
} else {
// Interpolate
// Calculate sub-octave coordinates
int margin = 2;
int64_t si0 = (i0 >> 1) - margin;
int64_t si1 = ((i1 - 1) >> 1) + margin + 1;
// Get sub-octave data
gaborator::pod_vector<T> sub_data(si1 - si0);
T *p = sub_data.data();
p = resample2_p2xf(source, p2_transform(xf.e + 1, xf.origin),
si0, si1, interpolate, p);
assert(p == sub_data.data() + si1 - si0);
for (int64_t i = i0; i < i1; i++) {
int64_t si = (i >> 1) - si0;
T val;
if (i & 1) {
T v1 = sub_data[si - 1];
T v0 = sub_data[si];
v0 += sub_data[si + 1];
v1 += sub_data[si + 2];
val =
v0 * (T)0.5625 +
v1 * (T)-0.0625;
} else {
val = sub_data[si];
}
*out++ = val;
}
}
} else {
// e == 0
out = source(xf.origin + i0, xf.origin + i1, out);
}
return out;
}
// As above, but taking an affine_transform.
template <class S, class OI>
OI resample2(const S &source, affine_transform lxf,
int64_t i0, int64_t i1,
bool interpolate, OI out)
{
p2_transform xf(lxf);
typedef typename std::iterator_traits<OI>::value_type T;
gaborator::pod_vector<T> data(i1 - i0);
T *p = data.data();
p = resample2_p2xf(source, xf, i0, i1, interpolate, p);
return std::copy(data.data(), data.data() + (i1 - i0), out);
}
// Calculate the range of source indices that will be accessed
// by a call to resample2(source, i0, i1, e) and return it
// through si0_ret and si1_ret.
// XXX this should take an "interpolate" argument so we don't
// return an unnecessarily large support when interpolation is off
inline void
resample2_support(affine_transform lxf, int64_t i0, int64_t i1,
int64_t &si0_ret, int64_t &si1_ret)
{
p2_transform xf(lxf);
int margin = 2;
if (xf.e > 0) {
// Note code duplication wrt resample2_p2xf().
// Also note tail recursion.
int64_t si0 = i0 * 2 - margin + 1;
int64_t si1 = i1 * 2 + margin;
resample2_support(zoom_p2(lxf, -1),
si0, si1, si0_ret, si1_ret);
} else if (xf.e < 0) {
int64_t si0 = (i0 >> 1) - margin;
int64_t si1 = ((i1 - 1) >> 1) + margin + 1;
resample2_support(zoom_p2(lxf, +1),
si0, si1, si0_ret, si1_ret);
} else {
si0_ret = xf.origin + i0;
si1_ret = xf.origin + i1;
}
}
// Inverse of the above, more or less: calculate the range of
// destination indices that depend on a given range of source indices.
inline void
resample2_inv_support(affine_transform lxf, int64_t si0, int64_t si1,
int64_t &i0_ret, int64_t &i1_ret)
{
p2_transform xf(lxf);
// Conservative
int margin = 2;
if (xf.e > 0) {
int64_t di0, di1;
resample2_inv_support(zoom_p2(lxf, -1),
si0, si1, di0, di1);
i0_ret = di0 >> 1;
i1_ret = (di1 >> 1) + 1;
} else if (xf.e < 0) {
int64_t di0, di1;
resample2_inv_support(zoom_p2(lxf, +1),
si0, si1, di0, di1);
i0_ret = di0 * 2 - margin + 1;
i1_ret = di1 * 2 + margin;
} else {
i0_ret = si0 - xf.origin;
i1_ret = si1 - xf.origin;
}
}
// Class wrappers for compatibility with other resamplers.
// Lanczos2 power-of-two resampler
struct lanczos2_pow2_resampler {
lanczos2_pow2_resampler(affine_transform xf_): xf(xf_) { }
template <class S, class OI>
OI operator()(const S &source, int64_t i0, int64_t i1, OI out) const {
return resample2(source, xf, i0, i1, true, out);
}
void support(int64_t i0, int64_t i1, int64_t &si0_ret, int64_t &si1_ret) const {
return resample2_support(xf, i0, i1, si0_ret, si1_ret);
}
void inv_support(int64_t si0, int64_t si1, int64_t &i0_ret, int64_t &i1_ret) {
return resample2_inv_support(xf, si0, si1, i0_ret, i1_ret);
}
affine_transform xf;
};
// Nearest-neighbor power-of-two resampler
// XXX simplify
struct nn_pow2_resampler {
nn_pow2_resampler(affine_transform xf_): xf(xf_){ }
template <class S, class OI>
OI operator()(const S &source, int64_t i0, int64_t i1, OI out) const {
return resample2(source, xf, i0, i1, false, out);
}
void support(int64_t i0, int64_t i1, int64_t &si0_ret, int64_t &si1_ret) const {
return resample2_support(xf, i0, i1, si0_ret, si1_ret);
}
void inv_support(int64_t si0, int64_t si1, int64_t &i0_ret, int64_t &i1_ret) {
return resample2_inv_support(xf, si0, si1, i0_ret, i1_ret);
}
affine_transform xf;
};
} // namespace
#endif

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//
// Vector math operations
//
// Copyright (C) 2016-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_VECTOR_MATH_H
#define _GABORATOR_VECTOR_MATH_H
#include <assert.h>
#if GABORATOR_USE_SSE3_INTRINSICS
#include <pmmintrin.h>
#endif
#include <complex>
namespace gaborator {
// The _naive versions are used when SSE is not available, and as
// references when testing the SSE versions
// Naive or not, this is faster than the macOS std::complex
// multiplication operator, which checks for infinities even with
// -ffast-math.
template <class T>
std::complex<T> complex_mul_naive(std::complex<T> a,
std::complex<T> b)
{
return std::complex<T>(a.real() * b.real() - a.imag() * b.imag(),
a.real() * b.imag() + a.imag() * b.real());
}
#if GABORATOR_USE_SSE3_INTRINSICS
// Note: this is sometimes slower than the naive code.
static inline
std::complex<double> complex_mul(std::complex<double> a_,
std::complex<double> b_)
{
__v2df a = _mm_setr_pd(a_.real(), a_.imag());
__v2df b = _mm_setr_pd(b_.real(), b_.imag());
__v2df as = (__v2df) _mm_shuffle_pd(a, a, 0x1);
__v2df t0 = _mm_mul_pd(a, _mm_shuffle_pd(b, b, 0x0));
__v2df t1 = _mm_mul_pd(as, _mm_shuffle_pd(b, b, 0x3));
__v2df c = __builtin_ia32_addsubpd(t0, t1); // SSE3
return std::complex<double>(c[0], c[1]);
}
#else
static inline
std::complex<double> complex_mul(std::complex<double> a_,
std::complex<double> b_)
{
return complex_mul_naive(a_, b_);
}
#endif
static inline
std::complex<float> complex_mul(std::complex<float> a_,
std::complex<float> b_)
{
return complex_mul_naive(a_, b_);
}
template <class T, class U, class V>
static inline void
elementwise_product_naive(T *r,
U *a,
V *b,
size_t n)
{
for (size_t i = 0; i < n; i++)
r[i] = complex_mul(a[i], b[i]);
}
template <class T, class U, class V, class S>
static inline void
elementwise_product_times_scalar_naive(T *r,
U *a,
V *b,
S s,
size_t n)
{
for (size_t i = 0; i < n; i++)
r[i] = a[i] * b[i] * s;
}
// I is the input complex data type, O is the output data type
template <class I, class O>
static inline void
complex_magnitude_naive(I *inv,
O *outv,
size_t n)
{
for (size_t i = 0; i < n; i++)
outv[i] = std::sqrt(inv[i].real() * inv[i].real() + inv[i].imag() * inv[i].imag());
}
#if GABORATOR_USE_SSE3_INTRINSICS
#include <pmmintrin.h>
// Perform two complex float multiplies in parallel
static inline
__v4sf complex_mul_vec2(__v4sf aa, __v4sf bb) {
__v4sf aas =_mm_shuffle_ps(aa, aa, 0xb1);
__v4sf t0 = _mm_mul_ps(aa, _mm_moveldup_ps(bb));
__v4sf t1 = _mm_mul_ps(aas, _mm_movehdup_ps(bb));
return __builtin_ia32_addsubps(t0, t1); // SSE3
}
// Calculate the elementwise product of a complex float vector
// and another complex float vector.
static inline void
elementwise_product(std::complex<float> *cv,
const std::complex<float> *av,
const std::complex<float> *bv,
size_t n)
{
assert((n & 1) == 0);
n >>= 1;
__v4sf *c = (__v4sf *) cv;
const __v4sf *a = (const __v4sf *) av;
const __v4sf *b = (const __v4sf *) bv;
while (n--) {
__v4sf aa = *a++;
__v4sf bb = *b++;
*c++ = complex_mul_vec2(aa, bb);
}
}
// Calculate the elementwise product of a complex float vector
// and real float vector.
//
// The input "a" may be unaligned; the output "c" must be aligned.
static inline void
elementwise_product(std::complex<float> *cv,
const std::complex<float> *av,
const float *bv,
size_t n)
{
assert((n & 3) == 0);
n >>= 2;
__v4sf *c = (__v4sf *) cv;
const __v4sf *a = (const __v4sf *) av;
const __v4sf *b = (const __v4sf *) bv;
while (n--) {
__v4sf a0 = (__v4sf) _mm_loadu_si128((const __m128i *) a++);
__v4sf a1 = (__v4sf) _mm_loadu_si128((const __m128i *) a++);
__v4sf bb = *b++;
*c++ = _mm_mul_ps(a0, _mm_unpacklo_ps(bb, bb));
*c++ = _mm_mul_ps(a1, _mm_unpackhi_ps(bb, bb));
}
}
static inline void
elementwise_product_times_scalar(std::complex<float> *cv,
const std::complex<float> *av,
const std::complex<float> *bv,
std::complex<float> d,
size_t n)
{
assert((n & 1) == 0);
n >>= 1;
const __v4sf *a = (const __v4sf *) av;
const __v4sf *b = (const __v4sf *) bv;
const __v4sf dd = (__v4sf) { d.real(), d.imag(), d.real(), d.imag() };
__v4sf *c = (__v4sf *) cv;
while (n--) {
__v4sf aa = *a++;
__v4sf bb = *b++;
*c++ = complex_mul_vec2(complex_mul_vec2(aa, bb), dd);
}
}
// XXX arguments reversed wrt others
static inline void
complex_magnitude(std::complex<float> *inv,
float *outv,
size_t n)
{
// Processes four complex values (32 bytes) at a time ,
// outputting four scalar magnitudes (16 bytes) at a time.
while ((((uintptr_t) inv) & 0x1F) && n) {
std::complex<float> v = *inv++;
*outv++ = std::sqrt(v.real() * v.real() + v.imag() * v.imag());
n--;
}
const __v4sf *in = (const __v4sf *) inv;
__v4sf *out = (__v4sf *) outv;
while (n >= 4) {
__v4sf aa = *in++; // c0re c0im c1re c1im
__v4sf aa2 = _mm_mul_ps(aa, aa); // c0re^2 c0im^2 c1re^2 c1im^2
__v4sf bb = *in++; // c2re c2im c3re c3im
__v4sf bb2 = _mm_mul_ps(bb, bb); // etc
// Gather the real parts: x0 x2 y0 y2
// 10 00 10 00 = 0x88
__v4sf re2 =_mm_shuffle_ps(aa2, bb2, 0x88);
__v4sf im2 =_mm_shuffle_ps(aa2, bb2, 0xdd);
__v4sf mag2 = _mm_add_ps(re2, im2);
__v4sf mag = __builtin_ia32_sqrtps(mag2);
// Unaligned store
_mm_storeu_si128((__m128i *)out, (__m128i)mag);
out++;
n -= 4;
}
inv = (std::complex<float> *) in;
outv = (float *)out;
while (n) {
std::complex<float> v = *inv++;
*outv++ = std::sqrt(v.real() * v.real() + v.imag() * v.imag());
n--;
}
}
// Double-precision version is unoptimized
static inline void
elementwise_product(std::complex<double> *c,
const std::complex<double> *a,
const std::complex<double> *b,
size_t n)
{
elementwise_product_naive(c, a, b, n);
}
static inline void
elementwise_product(std::complex<double> *c,
const std::complex<double> *a,
const double *b,
size_t n)
{
elementwise_product_naive(c, a, b, n);
}
template <class T, class U, class V, class S>
static inline void
elementwise_product_times_scalar(T *r,
U *a,
V *b,
S s,
size_t n)
{
elementwise_product_times_scalar_naive(r, a, b, s, n);
}
template <class O>
static inline void
complex_magnitude(std::complex<double> *inv,
O *outv,
size_t n)
{
complex_magnitude_naive(inv, outv, n);
}
#else // ! GABORATOR_USE_SSE3_INTRINSICS
// Forward to the naive implementations. These are inline functions
// rather than #defines to avoid namespace pollution.
template <class T, class U, class V>
static inline void
elementwise_product(T *r,
U *a,
V *b,
size_t n)
{
elementwise_product_naive(r, a, b, n);
}
template <class T, class U, class V, class S>
static inline void
elementwise_product_times_scalar(T *r,
U *a,
V *b,
S s,
size_t n)
{
elementwise_product_times_scalar_naive(r, a, b, s, n);
}
template <class I, class O>
static inline void
complex_magnitude(I *inv,
O *outv,
size_t n)
{
complex_magnitude_naive(inv, outv, n);
}
#endif // ! USE_SSE3_INTINSICS
} // namespace
#endif

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lib/gaborator/gaborator/version.h Normal file
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//
// Version number
//
// Copyright (C) 2015-2021 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_VERSION_H
#define _GABORATOR_VERSION_H
#define GABORATOR_VERSION_MAJOR 1
#define GABORATOR_VERSION_MINOR 7
#endif

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lib/pffft Submodule

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Subproject commit 28b56f5b0cc12960cba248bc98faf152d366f24d