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function [tfr,t,f] = tfrwv(x,t,N,trace);

%TFRWVWigner-Ville time-frequency distribution.

%[TFR,T,F]=TFRWV(X,T,N,TRACE) computes the Wigner-Ville distribution

%of a discrete-time signal X,

%or the cross Wigner-Ville representation between two signals.

%

%X : signal if auto-WV, or [X1,X2] if cross-WV.

%T : time instant(s) (default : 1:length(X)).

%N : number of frequency bins (default : length(X)).

%TRACE : if nonzero, the progression of the algorithm is shown

% (default : 0).

%TFR : time-frequency representation. When called without

% output arguments, TFRWV runs TFRQVIEW.

%F : vector of normalized frequencies.

%

%Example :

% sig=fmlin(128,0.1,0.4); tfrwv(sig);

%

%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.org

if (nargin == 0),

error('At least one parameter required');

end;

[xrow,xcol] = size(x);

if (nargin == 1),

t=1:xrow; N=xrow ; trace=0;

elseif (nargin == 2),

N=xrow ; trace=0;

elseif (nargin == 3),

trace = 0;

end;

if (N<0),

error('N must be greater than zero');

end;

[trow,tcol] = size(t);

if (xcol==0)|(xcol>2),

error('X must have one or two columns');

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;

tfr= zeros (N,tcol);

if trace, disp('Wigner-Ville distribution'); end;

for icol=1:tcol,

ti= t(icol); taumax=min([ti-1,xrow-ti,round(N/2)-1]);

tau=-taumax:taumax; indices= rem(N+tau,N)+1;

tfr(indices,icol) = x(ti+tau,1) .* conj(x(ti-tau,xcol));

tau=round(N/2);

if (ti<=xrow-tau)&(ti>=tau+1),

tfr(tau+1,icol) = 0.5 * (x(ti+tau,1) * conj(x(ti-tau,xcol)) + ...

x(ti-tau,1) * conj(x(ti+tau,xcol))) ;

end;

if trace, disprog(icol,tcol,10); end;

end;

tfr= fft(tfr);

if (xcol==1), tfr=real(tfr); end ;

if (nargout<=1),

tfrqview(tfr,x,t,'tfrwv');

elseif (nargout==3),

f=(0.5*(0:N-1)/N)';

end;