This class implements seven of the most popular spectral shape descriptors, computed on a linear scale for both amplitude and frequency. It is part of the Fluid Decomposition Toolkit of the FluCoMa project.FOOTNOTE:: This was made possible thanks to the FluCoMa project ( http://www.flucoma.org/ ) funded by the European Research Council ( https://erc.europa.eu/ ) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 725899).::
The descriptors are:
LIST::
##the four first statistical moments (https://en.wikipedia.org/wiki/Moment_(mathematics) ), more commonly known as:
LIST::
## the spectral centroid (1) in spectral bins as units. This is the point that splits the spectrum in 2 halves of equal energy. It is the weighted average of the magnitude spectrum.
## the spectral spread (2) in spectral bins. This is the standard deviation of the spectrum envelop, or the average of the distance to the centroid.
## the normalised skewness (3) as ratio. This indicates how tilted is the spectral curve in relation to the middle of the spectral frame, i.e. half of the Nyquist frequency. If it is below the bin representing that frequency, i.e. the central bin of the magnitude spectrum, it is positive.
## the normalised kurtosis (4) as ratio. This indicates how focused is the spectral curve. If it is peaky, it is high.
::
## the rolloff (5) in bin number. This indicates the bin under which 95% of the energy is included.
## the flatness (6) in dB. This is the ratio of geometric mean of the magnitude, over the arithmetic mean of the magnitudes. It yields a very approximate measure on how noisy a signal is.
## the crest (7) in dB. This is the ratio of the loudest magnitude over the RMS of the whole frame. A high number is an indication of a loud peak poking out from the overal spectral curve.
The drawings in Peeters 2003 (http://recherche.ircam.fr/anasyn/peeters/ARTICLES/Peeters_2003_cuidadoaudiofeatures.pdf) are useful, as are the commented examples below. For the mathematically-inclined reader, the tutorials and code offered here (https://www.audiocontentanalysis.org/) are interesting to further the understanding.
::
This class implements a classic spectral descriptor, the Mel-Frequency Cepstral Coefficients (https://en.wikipedia.org/wiki/Mel-frequency_cepstrum). The input is first decomposed in STRONG::numBands:: perceptually space bands, as in LINK::Classes/FluidMelBands::. It is then analysed in STRONG::numCoefs:: number of cepstral coefficients. It has the avantage to be amplitude invarient, except for the first coefficient. It is part of the Fluid Decomposition Toolkit of the FluCoMa project.FOOTNOTE:: This was made possible thanks to the FluCoMa project ( http://www.flucoma.org/ ) funded by the European Research Council ( https://erc.europa.eu/ ) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 725899).::
The process will return a multichannel buffer with the seven channels per input channel, each containing the 7 shapes. Each sample represents a value, which is every hopSize.
The process will return a single multichannel buffer of STRONG::numCoefs:: per input channel. Each frame represents a value, which is every hopSize.
CLASSMETHODS::
@ -49,25 +32,25 @@ ARGUMENT:: numChans
For multichannel srcBuf, how many channel should be processed.
ARGUMENT:: features
The destination buffer for the 7 spectral features describing the spectral shape.
The destination buffer for the numCoefs coefficients describing the spectral shape.
ARGUMENT:: numCoefs
(describe argument here)
The number of cepstral coefficients to be outputed. It will decide how many channels are produce per channel of the source.
ARGUMENT:: numBands
(describe argument here)
The number of bands that will be perceptually equally distributed between STRONG::minFreq:: and STRONG::maxFreq::.
ARGUMENT:: minFreq
(describe argument here)
The lower boundary of the lowest band of the model, in Hz.
ARGUMENT:: maxFreq
(describe argument here)
The highest boundary of the highest band of the model, in Hz.
ARGUMENT:: winSize
The window size. As sinusoidal estimation relies on spectral frames, we need to decide what precision we give it spectrally and temporally, in line with Gabor Uncertainty principles. http://www.subsurfwiki.org/wiki/Gabor_uncertainty
The window size. As MFCC computation relies on spectral frames, we need to decide what precision we give it spectrally and temporally, in line with Gabor Uncertainty principles. http://www.subsurfwiki.org/wiki/Gabor_uncertainty
ARGUMENT:: hopSize
The window hope size. As sinusoidal estimation relies on spectral frames, we need to move the window forward. It can be any size but low overlap will create audible artefacts.
The window hop size. As MFCC computation relies on spectral frames, we need to move the window forward. It can be any size but low overlap will create audible artefacts.
ARGUMENT:: fftSize
The inner FFT/IFFT size. It should be at least 4 samples long, at least the size of the window, and a power of 2. Making it larger allows an oversampling of the spectral precision.
@ -83,7 +66,7 @@ EXAMPLES::
code::
// create some buffers
(
b = Buffer.read(s,File.realpath(FluidBufSpectralShape.class.filenameSymbol).dirname.withTrailingSlash ++ "../AudioFiles/Nicol-LoopE-M.wav");
b = Buffer.read(s,File.realpath(FluidBufMFCC.class.filenameSymbol).dirname.withTrailingSlash ++ "../AudioFiles/Nicol-LoopE-M.wav");
For multichannel srcBuf, how many channel should be processed.
ARGUMENT:: features
The destination buffer for the 7 spectral features describing the spectral shape.
The destination buffer for the STRONG::numBands:: amplitudes describing the spectral shape.
ARGUMENT:: numBands
The number of bands that will be perceptually equally distributed between STRONG::minFreq:: and STRONG::maxFreq::. It will decide how many channels are produce per channel of the source.
This class implements seven of the most popular spectral shape descriptors, computed on a linear scale for both amplitude and frequency. It is part of the Fluid Decomposition Toolkit of the FluCoMa project.FOOTNOTE:: This was made possible thanks to the FluCoMa project ( http://www.flucoma.org/ ) funded by the European Research Council ( https://erc.europa.eu/ ) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 725899).::
The descriptors are:
LIST::
##the four first statistical moments (https://en.wikipedia.org/wiki/Moment_(mathematics) ), more commonly known as:
LIST::
## the spectral centroid (1) in spectral bins as units. This is the point that splits the spectrum in 2 halves of equal energy. It is the weighted average of the magnitude spectrum.
## the spectral spread (2) in spectral bins. This is the standard deviation of the spectrum envelop, or the average of the distance to the centroid.
## the normalised skewness (3) as ratio. This indicates how tilted is the spectral curve in relation to the middle of the spectral frame, i.e. half of the Nyquist frequency. If it is below the bin representing that frequency, i.e. the central bin of the magnitude spectrum, it is positive.
## the normalised kurtosis (4) as ratio. This indicates how focused is the spectral curve. If it is peaky, it is high.
::
## the rolloff (5) in bin number. This indicates the bin under which 95% of the energy is included.
## the flatness (6) in dB. This is the ratio of geometric mean of the magnitude, over the arithmetic mean of the magnitudes. It yields a very approximate measure on how noisy a signal is.
## the crest (7) in dB. This is the ratio of the loudest magnitude over the RMS of the whole frame. A high number is an indication of a loud peak poking out from the overal spectral curve.
The drawings in Peeters 2003 (http://recherche.ircam.fr/anasyn/peeters/ARTICLES/Peeters_2003_cuidadoaudiofeatures.pdf) are useful, as are the commented examples below. For the mathematically-inclined reader, the tutorials and code offered here (https://www.audiocontentanalysis.org/) are interesting to further the understanding.
::
This class implements a classic spectral descriptor, the Mel-Frequency Cepstral Coefficients (https://en.wikipedia.org/wiki/Mel-frequency_cepstrum). The input is first decomposed in STRONG::numBands:: perceptually space bands, as in LINK::Classes/FluidMelBands::. It is then analysed in STRONG::numCoefs:: number of cepstral coefficients. It has the avantage to be amplitude invarient, except for the first coefficient. It is part of the Fluid Decomposition Toolkit of the FluCoMa project.FOOTNOTE:: This was made possible thanks to the FluCoMa project ( http://www.flucoma.org/ ) funded by the European Research Council ( https://erc.europa.eu/ ) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 725899).::
The process will return a multichannel control steam with the seven values, which will be repeated if no change happens within the algorythm, i.e. when the hopSize is larger than the server's kr period.
The process will return a multichannel control steam of STRONG::maxNumCoefs::, which will be repeated if no change happens within the algorythm, i.e. when the hopSize is larger than the server's kr period.
CLASSMETHODS::
@ -33,25 +17,25 @@ ARGUMENT:: in
The audio to be processed.
ARGUMENT:: numCoefs
(describe argument here)
The number of cepstral coefficients to be outputed. It is limited by the maxNumCoefs parameter. When the number is smaller than the maximum, the output is zero-padded.
ARGUMENT:: numBands
(describe argument here)
The number of bands that will be perceptually equally distributed between minFreq and maxFreq to describe the spectral shape before it is converted to cepstral coefficients.
ARGUMENT:: minFreq
(describe argument here)
The lower boundary of the lowest band of the model, in Hz.
ARGUMENT:: maxFreq
(describe argument here)
The highest boundary of the highest band of the model, in Hz.
ARGUMENT:: maxNumCoefs
(describe argument here)
The maximum number of cepstral coefficients that can be computed. This sets the number of channels of the output, and therefore cannot be modulated.
ARGUMENT:: winSize
The window size. As sinusoidal estimation relies on spectral frames, we need to decide what precision we give it spectrally and temporally, in line with Gabor Uncertainty principles. http://www.subsurfwiki.org/wiki/Gabor_uncertainty
The window size. As MFCC computation relies on spectral frames, we need to decide what precision we give it spectrally and temporally, in line with Gabor Uncertainty principles. http://www.subsurfwiki.org/wiki/Gabor_uncertainty
ARGUMENT:: hopSize
The window hope size. As sinusoidal estimation relies on spectral frames, we need to move the window forward. It can be any size but low overlap will create audible artefacts. The -1 default value will default to half of winSize (overlap of 2).
The window hop size. As MFCC computation relies on spectral frames, we need to move the window forward. It can be any size but low overlap will create audible artefacts. The -1 default value will default to half of winSize (overlap of 2).
ARGUMENT:: fftSize
The inner FFT/IFFT size. It should be at least 4 samples long, at least the size of the window, and a power of 2. Making it larger allows an oversampling of the spectral precision. The -1 default value will default to windowSize.
@ -60,199 +44,87 @@ ARGUMENT:: maxFFTSize
How large can the FFT be, by allocating memory at instantiation time. This cannot be modulated.
RETURNS::
A 7-channel KR signal with the seven spectral shape descriptors. The latency is winSize.
A KR signal of STRONG::maxNumCoefs:: channels. The latency is winSize.
EXAMPLES::
code::
//create a monitoring bus for the descriptors
b = Bus.new(\control,0,7);
b = Bus.new(\control,0,13);
//create a monitoring window for the values
(
w = Window("Frequency Monitor", Rect(10, 10, 220, 190)).front;
c = Array.fill(7, {arg i; StaticText(w, Rect(10, i * 25 + 10, 135, 20)).background_(Color.grey(0.7)).align_(\right)});
c[0].string = ("Centroid: ");
c[1].string = ("Spread: ");
c[2].string = ("Skewness: ");
c[3].string = ("Kurtosis: ");
c[4].string = ("Rolloff: ");
c[5].string = ("Flatness: ");
c[6].string = ("Crest: ");
a = Array.fill(7, {arg i;
StaticText(w, Rect(150, i * 25 + 10, 60, 20)).background_(Color.grey(0.7)).align_(\center);
});
w = Window("MFCCs Monitor", Rect(10, 10, 420, 320)).front;
a = MultiSliderView(w,Rect(10, 10, 400, 300)).elasticMode_(1).isFilled_(1);
)
//run the wondow updating routine.
//run the window updating routine.
(
r = Routine {
{
b.get({ arg val;
{
if(w.isClosed.not) {
val.do({arg item,index;
a[index].string = item.round(0.01)})
a.value = val;
}
}.defer
});
0.01.wait;
}.loop
}.play
)
//play a simple sound to observe the values
(
{
var source;
source = BPF.ar(WhiteNoise.ar(), 330, 55/330);
Out.kr(b,FluidSpectralShape.kr(source));
source.dup;
}.play;
)
::
STRONG::A commented tutorial on how each descriptor behaves with test signals: ::
CODE::
// as above, create a monitoring bus for the descriptors
b = Bus.new(\control,0,7);
//again, create a monitoring window for the values
(
w = Window("Frequency Monitor", Rect(10, 10, 220, 190)).front;
c = Array.fill(7, {arg i; StaticText(w, Rect(10, i * 25 + 10, 135, 20)).background_(Color.grey(0.7)).align_(\right)});
c[0].string = ("Centroid: ");
c[1].string = ("Spread: ");
c[2].string = ("Skewness: ");
c[3].string = ("Kurtosis: ");
c[4].string = ("Rolloff: ");
c[5].string = ("Flatness: ");
c[6].string = ("Crest: ");
a = Array.fill(7, {arg i;
StaticText(w, Rect(150, i * 25 + 10, 60, 20)).background_(Color.grey(0.7)).align_(\center);
});
)
// this time, update a little more slowly, and convert in Hz the 3 descriptors published in bins by the algorythm.
// at 220, the centroid is on the frequency, the spread is narrow, but as wide as the FFT Hann window ripples, the skewness is high as we are low and therefore far left of the middle bin (aka half-Nyquist), the Kurtosis is incredibly high as we have a very peaky spectrum. The rolloff is slightly higher than the frequency, taking into account the FFT windowing ripples, the flatness is incredibly low, as we have one peak and not much else, and the crest is quite high, because most of the energy is in a few peaky bins.
x.set(\freq, 440)
// at 440, the skewness has changed (we are nearer the middle of the spectrogram) and the Kurtosis too, although it is still so high it is quite in the same order of magnitude. The rest is stable, as expected.
x.set(\freq, 11000)
// at 11kHz, kurtosis is still in the thousand, but skewness is almost null, as expected.
var source = Select.ar(type,[SinOsc.ar(220),Saw.ar(220),Pulse.ar(220)]) * LFTri.kr(0.1).exprange(0.01,0.1);
Out.kr(b,FluidMFCC.kr(source,maxNumCoefs:13));
source.dup;
}.play;
)
// white noise has a linear repartition of energy, so we would expect a centroid in the middle bin (aka half-Nyquist) with a spread covering the full range (+/- a quarter-Nyquist), with a skewness almost null since we are centered, and a very low Kurtosis since we are flat. The rolloff should be almost at Nyquist, the flatness as high as it gets, and the crest quite low.
// change the wave types, observe the amplitude invariance of the descriptors, apart from the leftmost coefficient
x.set(\type, 1)
// pink noise has a drop of 3dB per octave across the spectrum, so we would, by comparison, expect a lower centroid, a slighly higher skewness and kurtosis, a lower rolloff, a slighly lower flatness and a higher crest for the larger low-end energy.
x.set(\type, 2)
x.set(\type, 0)
// free this source
x.free
// third, bands of noise
// load a more exciting one
c = Buffer.read(s,File.realpath(FluidMelBands.class.filenameSymbol).dirname.withTrailingSlash ++ "../AudioFiles/Tremblay-AaS-SynthTwoVoices-M.wav");
// a second-order bandpass filter on whitenoise, centred on 330Hz with one octave bandwidth, gives us a centroid quite high. This is due to the exponential behaviour of the filter, with a gentle slope. Observe the spectral analyser:
// observe the number of bands. The unused ones at the top are not updated
x.set(\bands,20)
s.freqscope
// at first it seems quite centred, but then flip the argument FrqScl to lin(ear) and observe how high the spectrum goes. If we set it to a brickwall spectral filter tuned on the same frequencies:
x.set(\type, 1)
// back to the full range
x.set(\bands,40)
// we have a much narrower register, and our centroid and spread, as well as the kurtosis and flatness, agrees with this reading.
// focus all the bands on a mid range
x.set(\low,320, \high, 8000)
x.free
// focusing on the low end shows the fft resolution issue. One could restart the analysis with a larger fft to show more precision
// this example shows a similar result to the brickwall spectral bandpass above. If we move the central frequency nearer the half-Nyquist:
// free everything
x.free;b.free;c.free;r.stop;
::
x.set(\freq, 8800)
STRONG::A musical example::
// we can observe that the linear spread is kept the same, since there is the same linear distance in Hz between our frequencies. Skewness is a good indication here of where we are in the spectrum with the shape.
Pierre Alexandre Tremblay
7 years ago