function [x,mc,mn,mx]=v_melbankm(p,n,fs,fl,fh,w)
%V_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 v_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. See note (1) below.
%
%             '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]
%
% Outputs:	x     a sparse matrix containing the v_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 v_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: For legacy compatibility reasons, you must specify both or neither of mn and mx.
%
% Notes: (1) If 'ty' or 'ny' is specified, the total power in the fft is preserved.
%        (2) The filter shape (triangular, hamming etc) is defined in the mel (or erb etc) domain
%            rather than in the linear frequency domain which is more common (e.g. [2]).
%        (3) A mel-filterbank can also be created using v_filtbank() which uses triangular
%            filters in the linear frequency domain and copes better with the narrow filters
%            that arise when p is large on n is small.
%
% Examples of use:
%
% (a) Calcuate the Mel-frequency Cepstral Coefficients
%
%       f=v_rfft(s);			        % v_rfft() returns only 1+floor(n/2) coefficients
%		x=v_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]=v_melbankm(p,n,fs);   % na:nb gives the fft bins that are needed
%       z=log(x*(f(na:nb)).*conj(f(na:nb)));
%		c=dct(z);                   % take the DCT
%
% (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)
%
%      v_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: 185-19, 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): 357-366, Aug. 1980.


%      Copyright (C) Mike Brookes 1997-2009
%      Version: $Id: v_melbankm.m 10865 2018-09-21 17:22:45Z dmb $
%
%   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, in the comments, "FFT bin_0" assumes DC = bin 0 whereas "FFT bin_1" assumes DC = bin 1

if nargin < 6
    w='tz'; % default options
end
if nargin < 5 || isempty(fh)
    fh=0.5; % max freq is the nyquist
end
if nargin < 4 || isempty(fl)
    fl=0; % min freq is DC
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=v_frq2erb(mflh);       % convert frequency limits into erb-rate
        case 'b'
            mflh=v_frq2bark(mflh);      % convert frequency limits into bark
        otherwise
            mflh=v_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 filter 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=v_erb2frq(mflh(1)+[0 1 p p+1]*melinc)*n/fs;
    case 'b'
        blim=v_bark2frq(mflh(1)+[0 1 p p+1]*melinc)*n/fs;
    otherwise
        blim=v_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 filter_1 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=(v_frq2erb((b1:b4)*fs/n)-mflh(1))/melinc;
    case 'b'
        pf=(v_frq2bark((b1:b4)*fs/n)-mflh(1))/melinc;
    otherwise
        pf=(v_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=v_erb2frq(me);       % defining frequencies
            xg=v_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=v_bark2frq(me);      % defining frequencies
            xg=v_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=v_mel2frq(me);       % defining frequencies
            xg=v_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 (' v_xticksi 'Hz)']);
end