function [tfr,rtfr,hat] = tfrrgab(x,t,N,Nh,trace,K);%TFRRGAB Reassigned Gabor spectrogram time-frequency distribution.%	[TFR,RTFR,HAT] = TFRRGAB(X,T,N,NH,TRACE,K) %	computes the Gabor spectrogram and its reassigned version.%	This particular window (a Gaussian window) allows a 20 % faster%	algorithm than the TFRRSP function.%                  %	X     : analysed signal%	T     : the time instant(s)           (default : 1:length(X))%	N     : number of frequency bins      (default : length(X))%	NH    : length of the gaussian window (default : N/4))%	TRACE : if nonzero, the progression of the algorithm is shown%                                             (default : 0).%	K     : value at both extremities     (default 0.001)%	TFR,  : time-frequency representation and its reassigned%	RTFR    version. When called without output arguments, %	        TFRRGAB runs TFRQVIEW.%	HAT   : Complex matrix of the reassignment vectors.%%	Example :%	 sig=fmlin(128,0.1,0.4); tfrrgab(sig,1:128,128,19,1);%%	See also all the time-frequency representations listed in%	 the file CONTENTS (TFR*)%	F. Auger, May-July 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 (nargin <= 2), N=xrow;end;hlength=floor(N/4);hlength=hlength+1-rem(hlength,2);if (nargin == 1), t=1:xrow; end;if (nargin <= 3), Nh=hlength; trace=0; K=0.001;elseif (nargin == 4), trace = 0; K=0.001;elseif (nargin == 5), K= 0.001;end;if (N<0), error('N must be greater than zero');end;[trow,tcol] = size(t);if (xcol~=1), error('X must have only one column');elseif (trow~=1), error('T must only have one row'); elseif (2^nextpow2(N)~=N & nargin==6), fprintf('For a faster computation, N should be a power of two\n');end; if (rem(Nh,2)==0),  error('Nh must be odd'); elseif length(Nh)~=1, error('Nh must be a scalar');end;Nh2=Nh-2;continue=1;while continue, Nh2=Nh2+2; h=window(Nh2,'gauss',K^((Nh2-1)^2 /(Nh-1)^2));  continue=(h(Nh2)*(Nh2-1)>2*K);end;K=K^((Nh2-1)^2 /(Nh-1)^2); Nh=Nh2; Lh=(Nh-1)/2; h=h; Th=h.*[-Lh:Lh]';if (tcol==1), Dt=1; else Deltat=t(2:tcol)-t(1:tcol-1);  Mini=min(Deltat); Maxi=max(Deltat); if (Mini~=Maxi),  error('The time instants must be regularly sampled.'); else  Dt=Mini; end; clear Deltat Mini Maxi;end;tfr= zeros(N,tcol); tf2= zeros(N,tcol); tf3= zeros(N,tcol);if trace, disp('Gabor spectrogram'); end;for icol=1:tcol, if trace, disprog(icol,tcol,10); end; ti= t(icol);  tau=-min([round(N/2)-1,Lh,ti-1]):min([round(N/2)-1,Lh,xrow-ti]); indices= rem(N+tau,N)+1; norm_h=norm(h(Lh+1+tau)); tfr(indices,icol)=x(ti+tau).*conj( h(Lh+1+tau)) /norm_h; tf2(indices,icol)=x(ti+tau).*conj(Th(Lh+1+tau)) /norm_h;end ;tfr=fft(tfr); tf2=fft(tf2); avoid_warn=find(tfr~=0.0);tf3(avoid_warn)=round(imag(2*log(K)*N*tf2(avoid_warn)./tfr(avoid_warn)/(2.0*pi*Lh^2)));tf2(avoid_warn)=round(real(tf2(avoid_warn)./tfr(avoid_warn)/Dt));tfr=abs(tfr).^2;if trace, fprintf ('\nreassignment: \n'); end;rtfr= zeros(N,tcol); Ex=mean(abs(x(min(t):max(t))).^2); Threshold=1.0e-6*Ex;for icol=1:tcol, if trace, disprog(icol,tcol,10); end; for jcol=1:N,  if abs(tfr(jcol,icol))>Threshold,   icolhat= icol + tf2(jcol,icol);   icolhat=min(max(icolhat,1),tcol);   jcolhat= jcol - tf3(jcol,icol);   %while (jcolhat<1),jcolhat=jcolhat+N; end;   %while (jcolhat>N),jcolhat=jcolhat-N; end;   jcolhat=rem(rem(jcolhat-1,N)+N,N)+1;   rtfr(jcolhat,icolhat)=rtfr(jcolhat,icolhat) + tfr(jcol,icol) ;   tf2(jcol,icol)=jcolhat + j * icolhat;  else   tf2(jcol,icol)=inf*(1+j);   rtfr(jcol,icol)=rtfr(jcol,icol) + tfr(jcol,icol) ;  end; end;end;if trace, fprintf('\n'); end;clear tf3;if (nargout==0), continue=1; while (continue==1),  choice=menu ('Choose the representation:',...               'stop',...               'Gabor spectrogram',...               'reassigned Gabor spectrogram');  if (choice==1), continue=0;  elseif (choice==2),    Q=round(tcol*N/xrow);   tfrqview(tfr,x,t,'tfrgabor',tcol,Q,h);  elseif (choice==3),   tfrqview(rtfr,x,t,'tfrrgab',Nh);  end; end;elseif (nargout>2), hat=tf2;end;