gusucode.com > 《MATLAB图像与视频处理实用案例详解》代码 > 《MATLAB图像与视频处理实用案例详解》代码/第 19 章 基于语音识别的信号灯图像模拟控制技术/voicebox/melbankm.m
function [x,mc,mn,mx]=melbankm(p,n,fs,fl,fh,w)
%MELBANKM determine matrix for a mel/erb/bark-spaced filterbank [X,MN,MX]=(P,N,FS,FL,FH,W)
%
% Inputs:
% p number of filters in filterbank or the filter spacing in k-mel/bark/erb [ceil(4.6*log10(fs))]
% n length of fft
% fs sample rate in Hz
% fl low end of the lowest filter as a fraction of fs [default = 0]
% fh high end of highest filter as a fraction of fs [default = 0.5]
% w any sensible combination of the following:
% 'b' = bark scale instead of mel
% 'e' = erb-rate scale
% 'l' = log10 Hz frequency scale
% 'f' = linear frequency scale
%
% 'c' = fl/fh specify centre of low and high filters
% 'h' = fl/fh are in Hz instead of fractions of fs
% 'H' = fl/fh are in mel/erb/bark/log10
%
% 't' = triangular shaped filters in mel/erb/bark domain (default)
% 'n' = hanning shaped filters in mel/erb/bark domain
% 'm' = hamming shaped filters in mel/erb/bark domain
%
% 'z' = highest and lowest filters taper down to zero [default]
% 'y' = lowest filter remains at 1 down to 0 frequency and
% highest filter remains at 1 up to nyquist freqency
%
% 'u' = scale filters to sum to unity
%
% 's' = single-sided: do not double filters to account for negative frequencies
%
% 'g' = plot idealized filters [default if no output arguments present]
%
% Note that the filter shape (triangular, hamming etc) is defined in the mel (or erb etc) domain.
% Some people instead define an asymmetric triangular filter in the frequency domain.
%
% If 'ty' or 'ny' is specified, the total power in the fft is preserved.
%
% Outputs: x a sparse matrix containing the filterbank amplitudes
% If the mn and mx outputs are given then size(x)=[p,mx-mn+1]
% otherwise size(x)=[p,1+floor(n/2)]
% Note that the peak filter values equal 2 to account for the power
% in the negative FFT frequencies.
% mc the filterbank centre frequencies in mel/erb/bark
% mn the lowest fft bin with a non-zero coefficient
% mx the highest fft bin with a non-zero coefficient
% Note: you must specify both or neither of mn and mx.
%
% Examples of use:
%
% (a) Calcuate the Mel-frequency Cepstral Coefficients
%
% f=rfft(s); % rfft() returns only 1+floor(n/2) coefficients
% x=melbankm(p,n,fs); % n is the fft length, p is the number of filters wanted
% z=log(x*abs(f).^2); % multiply x by the power spectrum
% c=dct(z); % take the DCT
%
% (b) Calcuate the Mel-frequency Cepstral Coefficients efficiently
%
% f=fft(s); % n is the fft length, p is the number of filters wanted
% [x,mc,na,nb]=melbankm(p,n,fs); % na:nb gives the fft bins that are needed
% z=log(x*(f(na:nb)).*conj(f(na:nb)));
%
% (c) Plot the calculated filterbanks
%
% plot((0:floor(n/2))*fs/n,melbankm(p,n,fs)') % fs=sample frequency
%
% (d) Plot the idealized filterbanks (without output sampling)
%
% melbankm(p,n,fs);
%
% References:
%
% [1] S. S. Stevens, J. Volkman, and E. B. Newman. A scale for the measurement
% of the psychological magnitude of pitch. J. Acoust Soc Amer, 8: 185?9, 1937.
% [2] S. Davis and P. Mermelstein. Comparison of parametric representations for
% monosyllabic word recognition in continuously spoken sentences.
% IEEE Trans Acoustics Speech and Signal Processing, 28 (4): 357?66, Aug. 1980.
% Copyright (C) Mike Brookes 1997-2009
% Version: $Id: melbankm.m,v 1.11 2010/01/02 20:02:22 dmb Exp $
%
% VOICEBOX is a MATLAB toolbox for speech processing.
% Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You can obtain a copy of the GNU General Public License from
% http://www.gnu.org/copyleft/gpl.html or by writing to
% Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Note "FFT bin_0" assumes DC = bin 0 whereas "FFT bin_1" means DC = bin 1
if nargin < 6
w='tz'; % default options
if nargin < 5
fh=0.5; % max freq is the nyquist
if nargin < 4
fl=0; % min freq is DC
end
end
end
sfact=2-any(w=='s'); % 1 if single sided else 2
wr=' '; % default warping is mel
for i=1:length(w)
if any(w(i)=='lebf');
wr=w(i);
end
end
if any(w=='h') || any(w=='H')
mflh=[fl fh];
else
mflh=[fl fh]*fs;
end
if ~any(w=='H')
switch wr
case 'f' % no transformation
case 'l'
if fl<=0
error('Low frequency limit must be >0 for l option');
end
mflh=log10(mflh); % convert frequency limits into log10 Hz
case 'e'
mflh=frq2erb(mflh); % convert frequency limits into erb-rate
case 'b'
mflh=frq2bark(mflh); % convert frequency limits into bark
otherwise
mflh=frq2mel(mflh); % convert frequency limits into mel
end
end
melrng=mflh*(-1:2:1)'; % mel range
fn2=floor(n/2); % bin index of highest positive frequency (Nyquist if n is even)
if isempty(p)
p=ceil(4.6*log10(fs)); % default number of filters
end
if any(w=='c') % c option: specify fiter centres not edges
if p<1
p=round(melrng/(p*1000))+1;
end
melinc=melrng/(p-1);
mflh=mflh+(-1:2:1)*melinc;
else
if p<1
p=round(melrng/(p*1000))-1;
end
melinc=melrng/(p+1);
end
%
% Calculate the FFT bins corresponding to [filter#1-low filter#1-mid filter#p-mid filter#p-high]
%
switch wr
case 'f'
blim=(mflh(1)+[0 1 p p+1]*melinc)*n/fs;
case 'l'
blim=10.^(mflh(1)+[0 1 p p+1]*melinc)*n/fs;
case 'e'
blim=erb2frq(mflh(1)+[0 1 p p+1]*melinc)*n/fs;
case 'b'
blim=bark2frq(mflh(1)+[0 1 p p+1]*melinc)*n/fs;
otherwise
blim=mel2frq(mflh(1)+[0 1 p p+1]*melinc)*n/fs;
end
mc=mflh(1)+(1:p)*melinc; % mel centre frequencies
b1=floor(blim(1))+1; % lowest FFT bin_0 required might be negative)
b4=min(fn2,ceil(blim(4))-1); % highest FFT bin_0 required
%
% now map all the useful FFT bins_0 to filter1 centres
%
switch wr
case 'f'
pf=((b1:b4)*fs/n-mflh(1))/melinc;
case 'l'
pf=(log10((b1:b4)*fs/n)-mflh(1))/melinc;
case 'e'
pf=(frq2erb((b1:b4)*fs/n)-mflh(1))/melinc;
case 'b'
pf=(frq2bark((b1:b4)*fs/n)-mflh(1))/melinc;
otherwise
pf=(frq2mel((b1:b4)*fs/n)-mflh(1))/melinc;
end
%
% remove any incorrect entries in pf due to rounding errors
%
if pf(1)<0
pf(1)=[];
b1=b1+1;
end
if pf(end)>=p+1
pf(end)=[];
b4=b4-1;
end
fp=floor(pf); % FFT bin_0 i contributes to filters_1 fp(1+i-b1)+[0 1]
pm=pf-fp; % multiplier for upper filter
k2=find(fp>0,1); % FFT bin_1 k2+b1 is the first to contribute to both upper and lower filters
k3=find(fp<p,1,'last'); % FFT bin_1 k3+b1 is the last to contribute to both upper and lower filters
k4=numel(fp); % FFT bin_1 k4+b1 is the last to contribute to any filters
if isempty(k2)
k2=k4+1;
end
if isempty(k3)
k3=0;
end
if any(w=='y') % preserve power in FFT
mn=1; % lowest fft bin required (1 = DC)
mx=fn2+1; % highest fft bin required (1 = DC)
r=[ones(1,k2+b1-1) 1+fp(k2:k3) fp(k2:k3) repmat(p,1,fn2-k3-b1+1)]; % filter number_1
c=[1:k2+b1-1 k2+b1:k3+b1 k2+b1:k3+b1 k3+b1+1:fn2+1]; % FFT bin1
v=[ones(1,k2+b1-1) pm(k2:k3) 1-pm(k2:k3) ones(1,fn2-k3-b1+1)];
else
r=[1+fp(1:k3) fp(k2:k4)]; % filter number_1
c=[1:k3 k2:k4]; % FFT bin_1 - b1
v=[pm(1:k3) 1-pm(k2:k4)];
mn=b1+1; % lowest fft bin_1
mx=b4+1; % highest fft bin_1
end
if b1<0
c=abs(c+b1-1)-b1+1; % convert negative frequencies into positive
end
% end
if any(w=='n')
v=0.5-0.5*cos(v*pi); % convert triangles to Hanning
elseif any(w=='m')
v=0.5-0.46/1.08*cos(v*pi); % convert triangles to Hamming
end
if sfact==2 % double all except the DC and Nyquist (if any) terms
msk=(c+mn>2) & (c+mn<n-fn2+2); % there is no Nyquist term if n is odd
v(msk)=2*v(msk);
end
%
% sort out the output argument options
%
if nargout > 2
x=sparse(r,c,v);
if nargout == 3 % if exactly three output arguments, then
mc=mn; % delete mc output for legacy code compatibility
mn=mx;
end
else
x=sparse(r,c+mn-1,v,p,1+fn2);
end
if any(w=='u')
sx=sum(x,2);
x=x./repmat(sx+(sx==0),1,size(x,2));
end
%
% plot results if no output arguments or g option given
%
if ~nargout || any(w=='g') % plot idealized filters
ng=201; % 201 points
me=mflh(1)+(0:p+1)'*melinc;
switch wr
case 'f'
fe=me; % defining frequencies
xg=repmat(linspace(0,1,ng),p,1).*repmat(me(3:end)-me(1:end-2),1,ng)+repmat(me(1:end-2),1,ng);
case 'l'
fe=10.^me; % defining frequencies
xg=10.^(repmat(linspace(0,1,ng),p,1).*repmat(me(3:end)-me(1:end-2),1,ng)+repmat(me(1:end-2),1,ng));
case 'e'
fe=erb2frq(me); % defining frequencies
xg=erb2frq(repmat(linspace(0,1,ng),p,1).*repmat(me(3:end)-me(1:end-2),1,ng)+repmat(me(1:end-2),1,ng));
case 'b'
fe=bark2frq(me); % defining frequencies
xg=bark2frq(repmat(linspace(0,1,ng),p,1).*repmat(me(3:end)-me(1:end-2),1,ng)+repmat(me(1:end-2),1,ng));
otherwise
fe=mel2frq(me); % defining frequencies
xg=mel2frq(repmat(linspace(0,1,ng),p,1).*repmat(me(3:end)-me(1:end-2),1,ng)+repmat(me(1:end-2),1,ng));
end
v=1-abs(linspace(-1,1,ng));
if any(w=='n')
v=0.5-0.5*cos(v*pi); % convert triangles to Hanning
elseif any(w=='m')
v=0.5-0.46/1.08*cos(v*pi); % convert triangles to Hamming
end
v=v*sfact; % multiply by 2 if double sided
v=repmat(v,p,1);
if any(w=='y') % extend first and last filters
v(1,xg(1,:)<fe(2))=sfact;
v(end,xg(end,:)>fe(p+1))=sfact;
end
if any(w=='u') % scale to unity sum
dx=(xg(:,3:end)-xg(:,1:end-2))/2;
dx=dx(:,[1 1:ng-2 ng-2]);
vs=sum(v.*dx,2);
v=v./repmat(vs+(vs==0),1,ng)*fs/n;
end
plot(xg',v','b');
set(gca,'xlim',[fe(1) fe(end)]);
xlabel(['Frequency (' xticksi 'Hz)']);
end