Dawn@4: %  mfcc - Mel frequency cepstrum coefficient analysis.
Dawn@4: %   [ceps,freqresp,fb,fbrecon,freqrecon] = ...
Dawn@4: %			mfcc(input, samplingRate, [frameRate])
Dawn@4: % Find the cepstral coefficients (ceps) corresponding to the
Dawn@4: % input.  Four other quantities are optionally returned that
Dawn@4: % represent:
Dawn@4: %	the detailed fft magnitude (freqresp) used in MFCC calculation, 
Dawn@4: %	the mel-scale filter bank output (fb)
Dawn@4: %	the filter bank output by inverting the cepstrals with a cosine 
Dawn@4: %		transform (fbrecon),
Dawn@4: %	the smooth frequency response by interpolating the fb reconstruction 
Dawn@4: %		(freqrecon)
Dawn@4: %  -- Malcolm Slaney, August 1993
Dawn@4: % Modified a bit to make testing an algorithm easier... 4/15/94
Dawn@4: % Fixed Cosine Transform (indices of cos() were swapped) - 5/26/95
Dawn@4: % Added optional frameRate argument - 6/8/95
Dawn@4: % Added proper filterbank reconstruction using inverse DCT - 10/27/95
Dawn@4: % Added filterbank inversion to reconstruct spectrum - 11/1/95
Dawn@4: 
Dawn@4: % (c) 1998 Interval Research Corporation  
Dawn@4: 
Dawn@4: function [ceps,freqresp,fb,fbrecon,freqrecon] = ...
Dawn@4: 		mfcc(input, samplingRate, frameRate)
Dawn@4: global mfccDCTMatrix mfccFilterWeights
Dawn@4: 
Dawn@4: [r c] = size(input);
Dawn@4: if (r > c) 
Dawn@4: 	input=input';
Dawn@4: end
Dawn@4: 
Dawn@4: %	Filter bank parameters
Dawn@4: lowestFrequency = 133.3333;
Dawn@4: linearFilters = 13;
Dawn@4: linearSpacing = 66.66666666;
Dawn@4: logFilters = 27;
Dawn@4: logSpacing = 1.0711703;
Dawn@4: fftSize = 512;
Dawn@4: cepstralCoefficients = 13;
Dawn@4: windowSize = 400;
Dawn@4: windowSize = 256;		% Standard says 400, but 256 makes more sense
Dawn@4: 				% Really should be a function of the sample
Dawn@4: 				% rate (and the lowestFrequency) and the
Dawn@4: 				% frame rate.
Dawn@4: if (nargin < 2) samplingRate = 16000; end;
Dawn@4: if (nargin < 3) frameRate = 100; end;
Dawn@4: 
Dawn@4: % Keep this around for later....
Dawn@4: totalFilters = linearFilters + logFilters;
Dawn@4: 
Dawn@4: % Now figure the band edges.  Interesting frequencies are spaced
Dawn@4: % by linearSpacing for a while, then go logarithmic.  First figure
Dawn@4: % all the interesting frequencies.  Lower, center, and upper band
Dawn@4: % edges are all consequtive interesting frequencies. 
Dawn@4: 
Dawn@4: freqs = lowestFrequency + (0:linearFilters-1)*linearSpacing;
Dawn@4: freqs(linearFilters+1:totalFilters+2) = ...
Dawn@4: 		      freqs(linearFilters) * logSpacing.^(1:logFilters+2);
Dawn@4: 
Dawn@4: lower = freqs(1:totalFilters);
Dawn@4: center = freqs(2:totalFilters+1);
Dawn@4: upper = freqs(3:totalFilters+2);
Dawn@4: 
Dawn@4: % We now want to combine FFT bins so that each filter has unit
Dawn@4: % weight, assuming a triangular weighting function.  First figure
Dawn@4: % out the height of the triangle, then we can figure out each 
Dawn@4: % frequencies contribution
Dawn@4: mfccFilterWeights = zeros(totalFilters,fftSize);
Dawn@4: triangleHeight = 2./(upper-lower);
Dawn@4: fftFreqs = (0:fftSize-1)/fftSize*samplingRate;
Dawn@4: 
Dawn@4: for chan=1:totalFilters
Dawn@4: 	mfccFilterWeights(chan,:) = ...
Dawn@4:   (fftFreqs > lower(chan) & fftFreqs <= center(chan)).* ...
Dawn@4:    triangleHeight(chan).*(fftFreqs-lower(chan))/(center(chan)-lower(chan)) + ...
Dawn@4:   (fftFreqs > center(chan) & fftFreqs < upper(chan)).* ...
Dawn@4:    triangleHeight(chan).*(upper(chan)-fftFreqs)/(upper(chan)-center(chan));
Dawn@4: end
Dawn@4: %semilogx(fftFreqs,mfccFilterWeights')
Dawn@4: %axis([lower(1) upper(totalFilters) 0 max(max(mfccFilterWeights))])
Dawn@4: 
Dawn@4: hamWindow = 0.54 - 0.46*cos(2*pi*(0:windowSize-1)/windowSize);
Dawn@4: 
Dawn@4: if 0					% Window it like ComplexSpectrum
Dawn@4: 	windowStep = samplingRate/frameRate;
Dawn@4: 	a = .54;
Dawn@4: 	b = -.46;
Dawn@4: 	wr = sqrt(windowStep/windowSize);
Dawn@4: 	phi = pi/windowSize;
Dawn@4: 	hamWindow = 2*wr/sqrt(4*a*a+2*b*b)* ...
Dawn@4: 		(a + b*cos(2*pi*(0:windowSize-1)/windowSize + phi));
Dawn@4: end
Dawn@4: 
Dawn@4: % Figure out Discrete Cosine Transform.  We want a matrix
Dawn@4: % dct(i,j) which is totalFilters x cepstralCoefficients in size.
Dawn@4: % The i,j component is given by 
Dawn@4: %                cos( i * (j+0.5)/totalFilters pi )
Dawn@4: % where we have assumed that i and j start at 0.
Dawn@4: mfccDCTMatrix = 1/sqrt(totalFilters/2)*cos((0:(cepstralCoefficients-1))' * ...
Dawn@4: 				(2*(0:(totalFilters-1))+1) * pi/2/totalFilters);
Dawn@4: mfccDCTMatrix(1,:) = mfccDCTMatrix(1,:) * sqrt(2)/2;
Dawn@4: 
Dawn@4: %imagesc(mfccDCTMatrix);
Dawn@4: 
Dawn@4: % Filter the input with the preemphasis filter.  Also figure how
Dawn@4: % many columns of data we will end up with.
Dawn@4: if 1
Dawn@4: 	preEmphasized = filter([1 -.97], 1, input);
Dawn@4: else
Dawn@4: 	preEmphasized = input;
Dawn@4: end
Dawn@4: windowStep = samplingRate/frameRate;
Dawn@4: cols = fix((length(input)-windowSize)/windowStep);
Dawn@4: 
Dawn@4: % Allocate all the space we need for the output arrays.
Dawn@4: ceps = zeros(cepstralCoefficients, cols);
Dawn@4: if (nargout > 1) freqresp = zeros(fftSize/2, cols); end;
Dawn@4: if (nargout > 2) fb = zeros(totalFilters, cols); end;
Dawn@4: 
Dawn@4: % Invert the filter bank center frequencies.  For each FFT bin
Dawn@4: % we want to know the exact position in the filter bank to find
Dawn@4: % the original frequency response.  The next block of code finds the
Dawn@4: % integer and fractional sampling positions.
Dawn@4: if (nargout > 4)
Dawn@4: 	fr = (0:(fftSize/2-1))'/(fftSize/2)*samplingRate/2;
Dawn@4: 	j = 1;
Dawn@4: 	for i=1:(fftSize/2)
Dawn@4: 		if fr(i) > center(j+1)
Dawn@4: 			j = j + 1;
Dawn@4: 		end
Dawn@4: 		if j > totalFilters-1
Dawn@4: 			j = totalFilters-1;
Dawn@4: 		end
Dawn@4: 		fr(i) = min(totalFilters-.0001, ...
Dawn@4: 		    max(1,j + (fr(i)-center(j))/(center(j+1)-center(j))));
Dawn@4: 	end
Dawn@4: 	fri = fix(fr);
Dawn@4: 	frac = fr - fri;
Dawn@4: 
Dawn@4: 	freqrecon = zeros(fftSize/2, cols);
Dawn@4: end
Dawn@4: 
Dawn@4: % Ok, now let's do the processing.  For each chunk of data:
Dawn@4: %    * Window the data with a hamming window,
Dawn@4: %    * Shift it into FFT order,
Dawn@4: %    * Find the magnitude of the fft,
Dawn@4: %    * Convert the fft data into filter bank outputs,
Dawn@4: %    * Find the log base 10,
Dawn@4: %    * Find the cosine transform to reduce dimensionality.
Dawn@4: for start=0:cols-1
Dawn@4:     first = start*windowStep + 1;
Dawn@4:     last = first + windowSize-1;
Dawn@4:     fftData = zeros(1,fftSize);
Dawn@4:     fftData(1:windowSize) = preEmphasized(first:last).*hamWindow;
Dawn@4:     fftMag = abs(fft(fftData));
Dawn@4:     earMag = log10(mfccFilterWeights * fftMag');
Dawn@4: 
Dawn@4:     ceps(:,start+1) = mfccDCTMatrix * earMag;
Dawn@4:     if (nargout > 1) freqresp(:,start+1) = fftMag(1:fftSize/2)'; end;
Dawn@4:     if (nargout > 2) fb(:,start+1) = earMag; end
Dawn@4: 	if (nargout > 3) 
Dawn@4: 		fbrecon(:,start+1) = ...
Dawn@4: 			mfccDCTMatrix(1:cepstralCoefficients,:)' * ...
Dawn@4: 			ceps(:,start+1);
Dawn@4: 	end
Dawn@4: 	if (nargout > 4)
Dawn@4: 		f10 = 10.^fbrecon(:,start+1);
Dawn@4: 		freqrecon(:,start+1) = samplingRate/fftSize * ...
Dawn@4: 			(f10(fri).*(1-frac) + f10(fri+1).*frac);
Dawn@4: 	end
Dawn@4: end
Dawn@4: 
Dawn@4: % OK, just to check things, let's also reconstruct the original FB
Dawn@4: % output.  We do this by multiplying the cepstral data by the transpose
Dawn@4: % of the original DCT matrix.  This all works because we were careful to
Dawn@4: % scale the DCT matrix so it was orthonormal.
Dawn@4: if 1 & (nargout > 3) 
Dawn@4: 	fbrecon = mfccDCTMatrix(1:cepstralCoefficients,:)' * ceps;
Dawn@4: %	imagesc(mt(:,1:cepstralCoefficients)*mfccDCTMatrix);
Dawn@4: end;
Dawn@4: 
Dawn@4: