function [tfr,rtfr,hat] = tfrrpwv(x,t,N,h,trace);%TFRRPWV Reassigned  pseudo Wigner-Ville distribution.%	[TFR,RTFR,HAT] = TFRRPWV(X,T,N,H,TRACE) %	computes the pseudo Wigner-Ville distribution%	and its reassigned version.% %	X     : analysed signal,%	T     : the time instant(s)      (default : 1:length(X)).%	N     : number of frequency bins (default : length(X)).%	H     : frequency smoothing window, H(0) being forced to 1%	                                 (default : Hamming(N/4)).%	TRACE : if nonzero, the progression of the algorithm is shown%	                                 (default : 0).%	TFR,  : time-frequency representation and its reassigned%	RTFR    version. When called without output arguments, %	        TFRRPWV runs TFRQVIEW.%	HAT   : Complex matrix of the reassignment vectors.%%	Example:%	 sig=fmlin(128,0.1,0.4); t=1:2:128;%	 h=window(17,'Kaiser'); tfrrpwv(sig,t,64,h,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 < 1), error('At least 1 parameter is required');elseif (nargin <= 2), N=xrow;end;hlength=floor(N/4);if (rem(hlength,2)==0), hlength=hlength+1;end;if (nargin == 1), t=1:xrow; h = window(hlength); trace=0;elseif (nargin == 2)|(nargin == 3), h = window(hlength); trace=0;elseif (nargin == 4), trace = 0;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), fprintf('For a faster computation, N should be a power of two\n');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;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);if trace, disp('Pseudo Wigner-Ville distribution'); end;Dh=dwindow(h);for icol=1:tcol, ti= t(icol); taumax=min([ti-1,xrow-ti,round(N/2)-1,Lh]); tau=-taumax:taumax; indices= rem(N+tau,N)+1; if trace, disprog(icol,tcol,10); end; tfr(indices,icol)= h(Lh+1+tau).*x(ti+tau).*conj(x(ti-tau)); tf2(indices,icol)=Dh(Lh+1+tau).*x(ti+tau).*conj(x(ti-tau)); tau=round(N/2);  if (ti<=xrow-tau)&(ti>=tau+1)&(tau<=Lh),  tfr(tau+1,icol) = 0.5 * ( h(Lh+1+tau) * x(ti+tau,1) * conj(x(ti-tau,xcol))  + ...                            h(Lh+1-tau) * x(ti-tau,1) * conj(x(ti+tau,xcol))) ;  tf2(tau+1,icol) = 0.5 * (Dh(Lh+1+tau) * x(ti+tau,1) * conj(x(ti-tau,xcol))  + ...                           Dh(Lh+1-tau) * x(ti-tau,1) * conj(x(ti+tau,xcol))) ; end;end ;tfr= real(fft(tfr)); tf2=imag(fft(tf2));avoid_warn=find(tfr~=0);tf2(avoid_warn)=round(N*tf2(avoid_warn)./tfr(avoid_warn)/(2.0*pi)); %tf2= round(N*imag(fft(tf2))./tfr/(2.0*pi)); 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,   jcolhat= jcol - tf2(jcol,icol);   jcolhat=rem(rem(jcolhat-1,N)+N,N)+1;   rtfr(jcolhat,icol)=rtfr(jcolhat,icol) + tfr(jcol,icol) ;   tf2(jcol,icol)=jcolhat;  else    tf2(jcol,icol)=inf;   rtfr(jcol,icol)=rtfr(jcol,icol) + tfr(jcol,icol) ;  end; end;end;if trace, fprintf('\n'); end;if (nargout==0), continue=1; while (continue==1),  choice=menu ('Choose the representation:',...               'stop',...               'pseudo Wigner-Ville distribution',...               'reassigned pseudo Wigner-Ville distribution');  if (choice==1), continue=0;  elseif (choice==2),    tfrqview(tfr,x,t,'tfrpwv',h);  elseif (choice==3),   tfrqview(rtfr,x,t,'tfrrpwv',h);  end; end;elseif (nargout>2), hat=tf2;end;