# spectralCrest

Spectral crest for audio signals and auditory spectrograms

## Description

example

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

example

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

[crest,spectralPeak,spectralMean] = spectralCrest(___) returns the spectral peak and spectral mean.

## Examples

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

crest = spectralCrest(audioIn,fs);

t = linspace(0,size(audioIn,1)/fs,size(crest,1));
plot(t,crest)
xlabel('Time (s)')
ylabel('Crest')

Read in an audio file and then calculate the mel spectrogram using the melSpectrogram function.

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

Calculate the crest of the mel spectrogram over time. Plot the results.

crest = spectralCrest(s,cf);

t = linspace(0,size(audioIn,1)/fs,size(crest,1));
plot(t,crest)
xlabel('Time (s)')
ylabel('Crest')

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

crest = spectralCrest(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(crest,1));
plot(t,crest)
xlabel('Time (s)')
ylabel('Crest')

Create a dsp.AudioFileReader object to read in audio data frame-by-frame. Create a dsp.SignalSink to log the spectral crest calculation.

logger = dsp.SignalSink;

In an audio stream loop:

1. Read in a frame of audio data.

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

3. Log the spectral crest for later plotting.

To calculate the spectral crest 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.

'Window',hamming(size(audioIn,1)), ...
'OverlapLength',0);
logger(crest)
end

plot(logger.Buffer)
ylabel('Crest')

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 spectralCrest.

• You want to calculate the spectral crest 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 crest 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);

crest = spectralCrest(audioBuffered,fs, ...
'Window',win, ...
'OverlapLength',0);
logger(crest)
end

end

Plot the logged data.

plot(logger.Buffer)
ylabel('Crest (Hz)')

## 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 crest is calculated for the one-sided power spectrum.

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

Data Types: char | string

## Output Arguments

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

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

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

## Algorithms

The spectral crest is calculated as described in [1]:

$\text{crest}=\frac{\mathrm{max}\left({s}_{k\in \left[{b}_{1},{b}_{2}\right]}\right)}{\frac{1}{{b}_{2}-{b}_{1}}\sum _{k={b}_{1}}^{{b}_{2}}{s}_{k}}$

where

• sk is the spectral value at bin k.

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

## References

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