function [tfr,rtfr,hat] = tfrrspwv(x,t,N,g,h,trace);%TFRSPWV Reassigned smoothed pseudo Wigner-Ville distribution.%	[TFR,RTFR,HAT] = TFRRSPWV(X,T,N,G,H,TRACE) %	computes the smoothed 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)).%	G     : time smoothing window, G(0) being forced to 1. %	                                 (default : Hamming(N/10)). %	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, %	         TFRRSPWV runs TFRQVIEW.%	HAT   : Complex matrix of the reassignment vectors.%%	Example :%	 sig=fmlin(128,0.05,0.15)+fmlin(128,0.3,0.4); t=1:2:128; %	 g=window(15,'Kaiser'); h=window(63,'Kaiser');  %	 tfrrspwv(sig,t,64,g,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.org if (nargin == 0), error('At least 1 parameter required');end;[xrow,xcol] = size(x);if (xcol~=1), error('X must have only one column');end;if (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; % g=g/sum(g);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;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('Smoothed pseudo Wigner-Ville distribution'); end;Dh=dwindow(h); % Tg=g.*[-Lg:Lg]'; for icol=1:tcol, ti= t(icol); taumax=min([ti+Lg-1,xrow-ti+Lg,round(N/2)-1,Lh]); if trace, disprog(icol,tcol,10); end; % tau=0 points= -min([Lg,xrow-ti]):min([Lg,ti-1]); g2=g(Lg+1+points); g2=g2/sum(g2); Tg2= g2 .* points.' ; xx= x(ti-points) .* conj(x(ti-points)); tfr(1,icol)= sum( g2 .* xx) ;  tf2(1,icol)= sum( Tg2 .* xx) ; tf3(1,icol)= Dh(Lh+1) * tfr(1,icol) ; for tau=1:taumax,  points= -min([Lg,xrow-ti-tau]):min([Lg,ti-tau-1]);  g2=g(Lg+1+points); g2=g2/sum(g2); Tg2= g2 .* points.' ;  xx=x(ti+tau-points,1) .* conj(x(ti-tau-points));  tfr(  1+tau,icol)= sum( g2 .* xx);  tf3(  1+tau,icol)=Dh(Lh+tau+1) * tfr(  1+tau,icol) ;  tfr(  1+tau,icol)= h(Lh+tau+1) * tfr(  1+tau,icol) ;  tf2(  1+tau,icol)= h(Lh+tau+1) * sum(Tg2 .* xx);  tfr(N+1-tau,icol)= sum( g2 .* conj(xx));  tf3(N+1-tau,icol)=Dh(Lh-tau+1) * tfr(N+1-tau,icol);  tfr(N+1-tau,icol)= h(Lh-tau+1) * tfr(N+1-tau,icol);  tf2(N+1-tau,icol)= h(Lh-tau+1) * sum(Tg2 .* conj(xx)); end;end;tfr=real(fft(tfr));tf2=real(fft(tf2));tf3=imag(fft(tf3));avoid_warn=find(tfr~=0);tf2(avoid_warn)=round(tf2(avoid_warn)./tfr(avoid_warn)/Dt);tf3(avoid_warn)=round(N*tf3(avoid_warn)./tfr(avoid_warn)/(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,   icolhat= icol - tf2(jcol,icol);   icolhat=min(max(icolhat,1),tcol);   jcolhat= jcol - tf3(jcol,icol);   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',...               'smoothed pseudo Wigner-Ville distribution',...               'reassigned smoothed pseudo Wigner-Ville distribution');  if (choice==1), continue=0;  elseif (choice==2),    tfrqview(tfr,x,t,'tfrspwv',g,h);  elseif (choice==3),   tfrqview(rtfr,x,t,'tfrrspwv',g,h);  end; end;elseif (nargout>2), hat=tf2;end;