```
function [wts,binfrqs] = fft2melmx(nfft, sr, nfilts, width, minfrq, maxfrq, htkmel, constamp)
% wts = fft2melmx(nfft, sr, nfilts, width, minfrq, maxfrq, htkmel, constamp)
% Generate a matrix of weights to combine FFT bins into Mel
% bins. nfft defines the source FFT size at sampling rate sr.
% Optional nfilts specifies the number of output bands required
% (else one per bark), and width is the constant width of each
% band relative to standard Mel (default 1).
% While wts has nfft columns, the second half are all zero.
% Hence, Mel spectrum is fft2melmx(nfft,sr)*abs(fft(xincols,nfft));
% minfrq is the frequency (in Hz) of the lowest band edge;
% default is 0, but 133.33 is a common standard (to skip LF).
% maxfrq is frequency in Hz of upper edge; default sr/2.
% You can exactly duplicate the mel matrix in Slaney's mfcc.m
% as fft2melmx(512, 8000, 40, 1, 133.33, 6855.5, 0);
% htkmel=1 means use HTK's version of the mel curve, not Slaney's.
% constamp=1 means make integration windows peak at 1, not sum to 1.
% 2004-09-05 dpwe@ee.columbia.edu based on fft2barkmx
if nargin < 2; sr = 8000; end
if nargin < 3; nfilts = 40; end
if nargin < 4; width = 1.0; end
if nargin < 5; minfrq = 0; end % default bottom edge at 0
if nargin < 6; maxfrq = sr/2; end % default top edge at nyquist
if nargin < 7; htkmel = 0; end
if nargin < 8; constamp = 0; end
wts = zeros(nfilts, nfft);
% Center freqs of each FFT bin
fftfrqs = [0:(nfft/2)]/nfft*sr;
% 'Center freqs' of mel bands - uniformly spaced between limits
minmel = hz2mel(minfrq, htkmel);
maxmel = hz2mel(maxfrq, htkmel);
binfrqs = mel2hz(minmel+[0:(nfilts+1)]/(nfilts+1)*(maxmel-minmel), htkmel);
binbin = round(binfrqs/sr*(nfft-1));
for i = 1:nfilts
% fs = mel2hz(i + [-1 0 1], htkmel);
fs = binfrqs(i+[0 1 2]);
% scale by width
fs = fs(2)+width*(fs - fs(2));
% lower and upper slopes for all bins
loslope = (fftfrqs - fs(1))/(fs(2) - fs(1));
hislope = (fs(3) - fftfrqs)/(fs(3) - fs(2));
% .. then intersect them with each other and zero
% wts(i,:) = 2/(fs(3)-fs(1))*max(0,min(loslope, hislope));
wts(i,1+[0:(nfft/2)]) = max(0,min(loslope, hislope));
% actual algo and weighting in feacalc (more or less)
% wts(i,:) = 0;
% ww = binbin(i+2)-binbin(i);
% usl = binbin(i+1)-binbin(i);
% wts(i,1+binbin(i)+[1:usl]) = 2/ww * [1:usl]/usl;
% dsl = binbin(i+2)-binbin(i+1);
% wts(i,1+binbin(i+1)+[1:(dsl-1)]) = 2/ww * [(dsl-1):-1:1]/dsl;
% need to disable weighting below if you use this one
end
if (constamp == 0)
% Slaney-style mel is scaled to be approx constant E per channel
wts = diag(2./(binfrqs(2+[1:nfilts])-binfrqs(1:nfilts)))*wts;
end
% Make sure 2nd half of FFT is zero
wts(:,(nfft/2+1):nfft) = 0;
% seems like a good idea to avoid aliasing
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = mel2hz(z, htk)
% f = mel2hz(z, htk)
% Convert 'mel scale' frequencies into Hz
% Optional htk = 1 means use the HTK formula
% else use the formula from Slaney's mfcc.m
% 2005-04-19 dpwe@ee.columbia.edu
if nargin < 2
htk = 0;
end
if htk == 1
f = 700*(10.^(z/2595)-1);
else
f_0 = 0; % 133.33333;
f_sp = 200/3; % 66.66667;
brkfrq = 1000;
brkpt = (brkfrq - f_0)/f_sp; % starting mel value for log region
logstep = exp(log(6.4)/27); % the magic 1.0711703 which is the ratio needed to get from 1000 Hz to 6400 Hz in 27 steps, and is *almost* the ratio between 1000 Hz and the preceding linear filter center at 933.33333 Hz (actually 1000/933.33333 = 1.07142857142857 and exp(log(6.4)/27) = 1.07117028749447)
linpts = (z < brkpt);
f = 0*z;
% fill in parts separately
f(linpts) = f_0 + f_sp*z(linpts);
f(~linpts) = brkfrq*exp(log(logstep)*(z(~linpts)-brkpt));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function z = hz2mel(f,htk)
% z = hz2mel(f,htk)
% Convert frequencies f (in Hz) to mel 'scale'.
% Optional htk = 1 uses the mel axis defined in the HTKBook
% otherwise use Slaney's formula
% 2005-04-19 dpwe@ee.columbia.edu
if nargin < 2
htk = 0;
end
if htk == 1
z = 2595 * log10(1+f/700);
else
% Mel fn to match Slaney's Auditory Toolbox mfcc.m
f_0 = 0; % 133.33333;
f_sp = 200/3; % 66.66667;
brkfrq = 1000;
brkpt = (brkfrq - f_0)/f_sp; % starting mel value for log region
logstep = exp(log(6.4)/27); % the magic 1.0711703 which is the ratio needed to get from 1000 Hz to 6400 Hz in 27 steps, and is *almost* the ratio between 1000 Hz and the preceding linear filter center at 933.33333 Hz (actually 1000/933.33333 = 1.07142857142857 and exp(log(6.4)/27) = 1.07117028749447)
linpts = (f < brkfrq);
z = 0*f;
% fill in parts separately
z(linpts) = (f(linpts) - f_0)/f_sp;
z(~linpts) = brkpt+(log(f(~linpts)/brkfrq))./log(logstep);
end
```