tfrcw.m

matlab应用实例。如：FIR、IIR数字滤波器设计等。

function [tfr,t,f] = tfrcw(x,t,N,g,h,sigma,trace);
%TFRCW	Choi-Williams time-frequency distribution.
%	[TFR,T,F]=TFRCW(X,T,N,G,H,SIGMA,TRACE) computes the Choi-Williams  
%	distribution of a discrete-time signal X, or the
%	cross Choi-Williams representation between two signals. 
% 
%	X     : signal if auto-CW, or [X1,X2] if cross-CW.
%	T     : 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)). 
%	SIGMA : kernel width             (default : 1)
%	TRACE : if nonzero, the progression of the algorithm is shown
%                                        (default : 0).
%	TFR   : time-frequency representation. When called without 
%         output arguments, TFRCW runs TFRQVIEW.
%	F     : vector of normalized frequencies.
%
%	Example:
%	 sig=fmlin(128,0.05,0.3)+fmlin(128,0.15,0.4);  
%	 g=tftb_window(9,'Kaiser'); h=tftb_window(27,'Kaiser'); 
%	 t=1:128; tfrcw(sig,t,128,g,h,3.6,1);
% 
%	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 
%	[e-mail]

if (nargin == 0),
 error('At least 1 parameter required');
end;
[xrow,xcol] = size(x);
if (xcol==0)|(xcol>2),
 error('X must have one or two columns');
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 = tftb_window(glength); h = tftb_window(hlength); sigma = 1.0; trace = 0;
elseif (nargin == 2)|(nargin == 3),
 g = tftb_window(glength); h = tftb_window(hlength); sigma = 1.0; trace = 0;
elseif (nargin == 4),
 h = tftb_window(hlength); sigma = 1.0; trace = 0;
elseif (nargin == 5),
 sigma = 1.0; trace = 0;
elseif (nargin == 6),
 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;
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 (sigma<=0.0),
 error('SIGMA must be strictly positive'); 
end;

normfac = 16.0*pi/sigma; spreadfac = 16.0/sigma;
taumax = min([round(N/2),Lh]); tau = 1:taumax; points = -Lg:Lg;
CWKer = exp(-kron( points.' .^2, 1.0 ./ (spreadfac*tau.^2)));
CWKer = diag(g) * CWKer;

tfr= zeros (N,tcol) ;  
if trace, disp('Choi-Williams distribution'); end;
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;
 tfr(1,icol)= x(ti,1) .* conj(x(ti,xcol));

 for tau=1:taumax,
  points= -min([Lg,xrow-ti-tau]):min([Lg,ti-tau-1]);
  g2 = CWKer(Lg+1+points,tau); g2=g2/sum(g2);
  R=sum(g2 .* x(ti+tau-points,1) .* conj(x(ti-tau-points,xcol)));
  tfr(  1+tau,icol)=h(Lh+tau+1)*R;
  R=sum(g2 .* x(ti-tau-points,1) .* conj(x(ti+tau-points,xcol)));
  tfr(N+1-tau,icol)=h(Lh-tau+1)*R;
 end;

 tau=round(N/2); 
 if (ti<=xrow-tau)&(ti>=tau+1)&(tau<=Lh),
  points= -min([Lg,xrow-ti-tau]):min([Lg,ti-tau-1]);
  g2 = CWKer(Lg+1+points,tau); g2=g2/sum(g2);
  tfr(tau+1,icol) = 0.5 * ...
   (h(Lh+tau+1)*sum(g2 .* x(ti+tau-points,1) .* conj(x(ti-tau-points,xcol)))+...
    h(Lh-tau+1)*sum(g2 .* x(ti-tau-points,1) .* conj(x(ti+tau-points,xcol))));
 end;
end; 

clear CWKer;

if trace, fprintf('\n'); end;
tfr= fft(tfr); 
if (xcol==1), tfr=real(tfr); end ;

if (nargout==0),
 tfrqview(tfr,x,t,'tfrcw',g,h,sigma);
elseif (nargout==3),
 f=(0.5*(0:N-1)/N)';
end;