The mfcc function follows the historically popular Auditory Toolbox implementation by Slaney. In this case, the mel bandpass filters are spaced linearly until 1 kHz and logarithmically thereafter. They also have a start point at 133.33 etc. Hz. The defaults spacing of the mel bands in the audioFeatureExtractor object follow the O'Shaughnessy formula. The default audioFeatureExtractor formulation is a bit more common now, especially for the mel spectrogram intermediate step.
What follows is one way to make the two implementations approximately equal. An alternative way to the below is to modify the mfcc function by setting the bandedges option.
Get the bandedges of the the Slaney implementation that the mfcc function uses.
bE = slaneybandedges();
Define your input and parameters.
[audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav");
win1 = hamming(round(0.03*fs),"periodic");
overlapLength = round(0.015*fs);
Get the default output of the mfcc function
mfcc_output = mfcc(audioIn,fs,LogEnergy="ignore");
Create an audioFeatureExtractor object and set the options to extract the same feature as mfcc function.
aFE = audioFeatureExtractor(SampleRate=fs, ...
Window=hamming(round(0.03*fs),"periodic"), ...
OverlapLength=round(0.02*fs), ...
mfcc=true, ...
FFTLength=numel(win1));
setExtractorParameters(aFE,"melSpectrum", ...
MelStyle="slaney", ...
SpectrumType="magnitude", ...
WindowNormalization=false, ...
FilterBankDesignDomain="linear", ...
FilterBankNormalization="bandwidth", ...
NumBands=40, ...
FrequencyRange=[bE(1),bE(end)])
features = extract(aFE,audioIn);
idx = info(aFE);
afe_output = features(:,idx.mfcc);
coeffToInspect = 1;
plot(afe_output(:,coeffToInspect),'bo'),hold on
plot(mfcc_output(:,coeffToInspect),'r*'),hold off
rms(afe_output(:)-mfcc_output(:))
Supporting Function
function bE = slaneybandedges()
% Default band edges as defined by the documentation for the
% Auditory Toolbox.
factor = 133.33333333333333;
bE = zeros(1,42);
for ii = 1:13
bE(ii) = factor + (factor/2)*(ii-1);
end
for ii = 14:42
bE(ii) = bE(ii-1)*1.0711703;
end
end
