Documentation

spectralKurtosis

Spectral kurtosis for audio signals and auditory spectrograms

Description

example

kurtosis = spectralKurtosis(x,f) returns the spectral kurtosis of the signal, x, over time. How the function interprets x depends on the shape of f.

example

kurtosis = spectralKurtosis(x,f,Name,Value) specifies options using one or more Name,Value pair arguments.

[kurtosis,spread,centroid] = spectralKurtosis(___) returns the spectral spread and spectral centroid.

Examples

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Read in an audio file, calculate the kurtosis using default parameters, and then plot the results.

kurtosis = spectralKurtosis(audioIn,fs);

t = linspace(0,size(audioIn,1)/fs,size(kurtosis,1));
plot(t,kurtosis)
xlabel('Time (s)')
ylabel('Kurtosis') Read in an audio file and then calculate the mel spectrogram using the melSpectrogram function. Calculate the kurtosis of the mel spectrogram over time. Plot the results.

[s,cf,t] = melSpectrogram(audioIn,fs);

kurtosis = spectralKurtosis(s,cf);

plot(t,kurtosis)
xlabel('Time (s)')
ylabel('Kurtosis') Read in an audio file.

Calculate the kurtosis of the power spectrum over time. Calculate the kurtosis for 50 ms Hamming windows of data with 25 ms overlap. Use the range from 62.5 Hz to fs/2 for the kurtosis calculation. Plot the results.

kurtosis = spectralKurtosis(audioIn,fs, ...
'Window',hamming(round(0.05*fs)), ...
'OverlapLength',round(0.025*fs), ...
'Range',[62.5,fs/2]);

t = linspace(0,size(audioIn,1)/fs,size(kurtosis,1));
plot(t,kurtosis)
xlabel('Time (s)')
ylabel('Kurtosis') Create a dsp.AudioFileReader object to read in audio data frame-by-frame. Create a dsp.SignalSink to log the spectral kurtosis calculation.

logger = dsp.SignalSink;

In an audio stream loop:

1. Read in a frame of audio data.

2. Calculate the spectral kurtosis for the frame of audio.

3. Log the spectral kurtosis for later plotting.

To calculate the spectral kurtosis for only a given input frame, specify a window with the same number of samples as the input, and set the overlap length to zero. Plot the logged data.

kurtosis = spectralKurtosis(audioIn,fileReader.SampleRate, ...
'Window',win, ...
'OverlapLength',0);
logger(kurtosis)
end

plot(logger.Buffer)
ylabel('Kurtosis') Use dsp.AsyncBuffer if

• The input to your audio stream loop has a variable samples-per-frame.

• The input to your audio stream loop has an inconsistent samples-per-frame with the analysis window of spectralKurtosis.

• You want to calculate the spectral kurtosis for overlapped data.

Create a dsp.AsyncBuffer object, reset the logger, and release the file reader.

buff = dsp.AsyncBuffer;
reset(logger)

Specify that the spectral kurtosis is calculated for 50 ms frames with a 25 ms overlap.

samplesPerFrame = round(fs*0.05);
samplesOverlap = round(fs*0.025);

samplesPerHop = samplesPerFrame - samplesOverlap;

win = hamming(samplesPerFrame);

write(buff,audioIn);

while buff.NumUnreadSamples >= samplesPerHop

kurtosis = spectralKurtosis(audioBuffered,fs, ...
'Window',win, ...
'OverlapLength',0);
logger(kurtosis)
end

end

Plot the logged data.

plot(logger.Buffer)
ylabel('Kurtosis') Input Arguments

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Input signal, specified as a vector, matrix, or 3-D array. How the function interprets x depends on the shape of f.

Data Types: single | double

Sample rate or frequency vector in Hz, specified as a scalar or vector, respectively. How the function interprets x depends on the shape of f:

• If f is a scalar, x is interpreted as a time-domain signal, and f is interpreted as the sample rate. In this case, x must be a real vector or matrix. If x is specified as a matrix, the columns are interpreted as individual channels.

• If f is a vector, x is interpreted as a frequency-domain signal, and f is interpreted as the frequencies, in Hz, corresponding to the rows of x. In this case, x must be a real L-by-M-by-N array, where L is the number of spectral values at given frequencies of f, M is the number of individual spectrums, and N is the number of channels.

• The number of rows of x, L, must be equal to the number of elements of f.

Data Types: single | double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'Window',hamming(256)

Note

The following name-value pair arguments apply if x is a time-domain signal. If x is a frequency-domain signal, name-value pair arguments are ignored.

Window applied in the time domain, specified as the comma-separated pair consisting of 'Window' and a real vector. The number of elements in the vector must be in the range [1, size(x,1)]. The number of elements in the vector must also be greater than OverlapLength.

Data Types: single | double

Number of samples overlapped between adjacent windows, specified as the comma-separated pair consisting of 'OverlapLength' and an integer in the range [0, size(Window,1)).

Data Types: single | double

Number of bins used to calculate the DFT of windowed input samples, specified as the comma-separated pair consisting of 'FFTLength' and a positive scalar integer. If unspecified, FFTLength defaults to the number of elements in the Window.

Data Types: single | double

Frequency range in Hz, specified as the comma-separated pair consisting of 'Range' and a two-element row vector of increasing real values in the range [0, f/2].

Data Types: single | double

Spectrum type, specified as the comma-separated pair consisting of 'SpectrumType' and 'power' or 'magnitude':

• 'power' –– The spectral kurtosis is calculated for the one-sided power spectrum.

• 'magnitude' –– The spectral kurtosis is calculated for the one-sided magnitude spectrum.

Data Types: char | string

Output Arguments

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Spectral kurtosis, returned as a scalar, vector, or matrix. Each row of kurtosis corresponds to the spectral kurtosis of a window of x. Each column of kurtosis corresponds to an independent channel.

Spectral spread, returned as a scalar, vector, or matrix. Each row of spread corresponds to the spectral spread of a window of x. Each column of spread corresponds to an independent channel.

Spectral centroid in Hz, returned as a scalar, vector, or matrix. Each row of centroid corresponds to the spectral centroid of a window of x. Each column of centroid corresponds to an independent channel.

Algorithms

The spectral kurtosis is calculated as described in :

$\text{kurtosis}=\frac{\sum _{k={b}_{1}}^{{b}_{2}}{\left({f}_{k}-{\mu }_{1}\right)}^{4}{s}_{k}}{{\left({\mu }_{2}\right)}^{4}\sum _{k={b}_{1}}^{{b}_{2}}{s}_{k}}$

where

• fk is the frequency in Hz corresponding to bin k.

• sk is the spectral value at bin k.

• b1 and b2 are the band edges, in bins, over which to calculate the spectral skewness.

• μ1 is the spectral centroid, calculated as described by the spectralCentroid function.

• μ2 is the spectral spread, calculated as described by the spectralSpread function.

 Peeters, G. "A Large Set of Audio Features for Sound Description (Similarity and Classification) in the CUIDADO Project." Technical Report; IRCAM: Paris, France, 2004.

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