function [tfr,rtfr,hat] = tfrrmsc(x,t,N,f0T,trace,K);%TFRRMSC Reassigned Morlet Scalogram time-frequency distribution.%	[TFR,RTFR,HAT] = TFRRMSC(X,T,N,F0T,TRACE) %	computes the Morlet scalogram and its reassigned version.%                  %	X     : analysed signal%	T     : the time instant(s)           (default : 1:length(X))%	N     : number of frequency bins      (default : length(X))%	F0T   : time-bandwidth product of the mother wavelet %					      (default : 2.5)) %	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, %	        TFRRMSC runs TFRQVIEW.%	HAT   : Complex matrix of the reassignment vectors.%%	Example :%	 sig=fmlin(64,0.1,0.4); tfrrmsc(sig,1:64,64,2.1,1);%%	See also all the time-frequency representations listed in%	 the file CONTENTS (TFR*)%	F. Auger, January, April 1996.%	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 (nargin == 1), t=1:xrow; N=xrow; f0T=2.5; trace=0; K= 0.001;elseif (nargin == 2),  N=xrow; f0T=2.5; trace=0; K= 0.001;elseif (nargin == 3), f0T=2.5; 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 (f0T<=0), error('F0T must be positive');elseif (length(f0T)~=1), error('F0T must be a scalar');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('Morlet Scalogram'); end;M=ceil(f0T*N*sqrt(2.0*log(1/K))); tau = 0:M+round(N/2); pi2 = 2.0*pi;hstar = exp(-(tau/(N*f0T)).^2 /2.0) .* exp(-j*pi2*tau/N);Thstar = tau.*hstar;for m=1:round(N/2)-1 if trace, disprog(m,N/2,10); end; factor=sqrt(m/(f0T*N)); for icol=1:tcol,   ti= t(icol);   tauneg=1:min([ceil(M/m),ti-1]);   taupos=0:min([ceil(M/m),xrow-ti]);   % positive frequencies   tfr(  1+m,icol)= hstar(1+taupos*m)*x(ti+taupos);   tf2(  1+m,icol)=Thstar(1+taupos*m)*x(ti+taupos);   if length(tauneg) > 0,    tfr(1+m,icol)=tfr(1+m,icol) + conj( hstar(1+tauneg*m))*x(ti-tauneg);    tf2(1+m,icol)=tf2(1+m,icol) - conj(Thstar(1+tauneg*m))*x(ti-tauneg);   end;   % negative frequencies   tfr(N+1-m,icol)=conj( hstar(1+taupos*m))*x(ti+taupos);   tf2(N+1-m,icol)=conj(Thstar(1+taupos*m))*x(ti+taupos);   if length(tauneg) > 0,    tfr(N+1-m,icol)=tfr(N+1-m,icol) +  hstar(1+tauneg*m)*x(ti-tauneg);    tf2(N+1-m,icol)=tf2(N+1-m,icol) - Thstar(1+tauneg*m)*x(ti-tauneg);   end; end; tfr(  1+m,:)=factor*tfr(  1+m,:); tf2(  1+m,:)=factor*tf2(  1+m,:)/m; tfr(N+1-m,:)=factor*tfr(N+1-m,:); tf2(N+1-m,:)=factor*tf2(N+1-m,:)/m;end;m=round(N/2); factor=sqrt(m/(f0T*N));if trace, disprog(m,N/2,10); endfor icol=1:tcol, ti= t(icol); tauneg=1:min([ceil(M/m),ti-1]); taupos=0:min([ceil(M/m),xrow-ti]); tfr(  1+m,icol)= hstar(1+taupos*m)*x(ti+taupos); tf2(  1+m,icol)=Thstar(1+taupos*m)*x(ti+taupos); if length(tauneg) > 0,  tfr(1+m,icol)=tfr(1+m,icol) + conj( hstar(1+tauneg*m))*x(ti-tauneg);  tf2(1+m,icol)=tf2(1+m,icol) - conj(Thstar(1+tauneg*m))*x(ti-tauneg); end;end;tfr(1+m,:)=factor*tfr(1+m,:); tf2(1+m,:)=factor*tf2(1+m,:)/m;avoid_warn=find(tfr~=0.0);tf2(avoid_warn)=tf2(avoid_warn)./tfr(avoid_warn); tfr=abs(tfr).^2;if trace, disp('reassignment :'); end;rtfr= zeros(N,tcol); Ex=mean(abs(x(min(t):max(t))).^2); Threshold=1.0e-6*Ex;factor=2.0*pi*N*f0T*f0T;for icol=1:tcol, if trace, disprog(icol,tcol,10); end; for jcol=1:N,  if tfr(jcol,icol)>Threshold,   icolhat= icol + round(real(tf2(jcol,icol)/Dt));   icolhat=min(max(icolhat,1),tcol);   m=rem(jcol+round(N/2)-2,N)-round(N/2)+1;   jcolhat= jcol + round(imag(m*m*tf2(jcol,icol)/factor));   jcolhat=rem(rem(jcolhat-1,N)+N,N)+1;   rtfr(jcolhat,icolhat)= rtfr(jcolhat,icolhat)+tfr(jcol,icol);   tf2(jcol,icol)= jcolhat + 1j * icolhat;  else   tf2(jcol,icol)=(1+j)*inf;   rtfr(jcol,icol)=rtfr(jcol,icol)+tfr(jcol,icol);  end; end;end;if (nargout==0), continue=1; while (continue==1),  choice=menu ('Choose the representation:',...               'stop',...               'Morlet scalogram',...               'reassigned Morlet scalogram');  if (choice==1), continue=0;  elseif (choice==2),    tfrqview(tfr,x,t,'tfrmsc',f0T);  elseif (choice==3),   tfrqview(rtfr,x,t,'tfrrmsc',f0T);  end; end;elseif (nargout>2), hat=tf2;end;