function [tfr,t,f] = tfrmhs(x,t,N,g,h,trace);%TFRMHS	Margenau-Hill-Spectrogram time-frequency distribution.%	[TFR,T,F]=TFRMHS(X,T,N,G,H,TRACE) computes the Margenau-Hill-Spectrogram %	distribution of a discrete-time signal X, or the cross%	Margenau-Hill-Spectrogram representation between two signals. % %	X     : Signal if auto-MHS, or [X1,X2] if cross-MHS.%	T     : time instant(s)          (default : 1:length(X)).%	N     : number of frequency bins (default : length(X)).%	G,H   : analysis windows, normalized so that the representation %               preserves the signal energy.%	                (default : Hamming(N/10) and Hamming(N/4)). %	TRACE : if nonzero, the progression of the algorithm is shown%                                        (default : 0).%	TFR   : time-frequency representation. When called without %               output arguments, TFRMHS runs TFRQVIEW.%	F     : vector of normalized frequencies.%%	Example:%	 sig=fmlin(128,0.1,0.4); g=window(21,'Kaiser'); %	 h=window(63,'Kaiser'); tfrmhs(sig,1:128,64,g,h,1);% %	See also all the time-frequency representations listed in%	 the file CONTENTS (TFR*)%	F. Auger, May-August 1994, July 1995.%	Copyright (c) 1996 by CNRS (France).%%	------------------- CONFIDENTIAL PROGRAM -------------------- %	This program can not be used without the authorization of its%	author(s). For any comment or bug report, please send e-mail to %	f.auger@ieee.orgif (nargin == 0), error('At least 1 parameter required');end;[xrow,xcol] = size(x);if (xcol==0)|(xcol>2), error('X must have one or two columns');endif (nargin <= 2), N=xrow;elseif (N<0), error('N must be greater than zero');elseif (2^nextpow2(N)~=N), fprintf('For a faster computation, N should be a power of two\n');end;hlength=floor(N/4); hlength=hlength+1-rem(hlength,2); glength=floor(N/10);glength=glength+1-rem(glength,2);if (nargin == 1), t=1:xrow; g = window(glength); h = window(hlength); trace = 0;elseif (nargin == 2)|(nargin == 3), g = window(glength); h = window(hlength); trace = 0;elseif (nargin == 4), h = window(hlength); trace = 0;elseif (nargin == 5), trace = 0;end;[trow,tcol] = size(t);if (trow~=1), error('T must only have one row'); end; [grow,gcol]=size(g); Lg=(grow-1)/2;if (gcol~=1)|(rem(grow,2)==0), error('G must be a smoothing window with odd length'); end;[hrow,hcol]=size(h); Lh=(hrow-1)/2; h=h/h(Lh+1);if (hcol~=1)|(rem(hrow,2)==0),  error('H must be a smoothing window with odd length');end;Lgh=min(Lg,Lh); points=-Lgh:Lgh; Kgh=sum(h(Lh+1+points).*conj(g(Lg+1+points))); h=h/Kgh;tfr= zeros (N,tcol); tfr2= zeros(N,tcol);if trace, disp('Pseudo Margenau-Hill distribution'); end;for icol=1:tcol, ti= t(icol); if trace, disprog(icol,tcol,10); end; tau=-min([round(N/2)-1,Lg,ti-1]):min([round(N/2)-1,Lg,xrow-ti]); indices= rem(N+tau,N)+1; tfr(indices,icol)=x(ti+tau,1).*conj(g(Lg+1+tau)); tau=-min([round(N/2)-1,Lh,ti-1]):min([round(N/2)-1,Lh,xrow-ti]); indices= rem(N+tau,N)+1; tfr2(indices,icol)=x(ti+tau,xcol).*conj(h(Lh+1+tau));end; if trace, fprintf('\n'); end;tfr=real(fft(tfr).*conj(fft(tfr2))); if (nargout==0), tfrqview(tfr,x,t,'tfrmhs',g,h);elseif (nargout==3), if rem(N,2)==0,   f=[0:N/2-1 -N/2:-1]'/N; else  f=[0:(N-1)/2 -(N-1)/2:-1]'/N;   end;end;