tfrwv.m

来自「时频分析工具箱」· M 代码 · 共 118 行

function [tfr,t,f] = tfrwv(x,t,N,trace);
%TFRWV	Wigner-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.                      %	输入信号为列向量
%	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 
%	[e-mail] 

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构成说明： t=1,2,3,...,254,255,256 
% (1)icol=1,第1列, ti=1, taumax=0,tau=0,indices=1
% tfr(1,1)=x(1,1)*x(1,1)=5.2786e5
% (2)icol=2,第2列, ti=2, taumax=1,tau=-1,0,1;indices=256,1,2
% tfr(256,2)=x(1,1)*x(3,1)=6.7026e5
% tfr(1,2)=x(2,1)*x(2,1)=7.7183e5
% tfr(2,2)=x(3,1)*x(1,1)=6.7026e5
% (3)icol=3,第3列, ti=3, taumax=2,tau=-2,-1,0,1,2;indices=255,256,1,2,3
% tfr(255,3)=x(1,1)*x(5,1)=7.6326e5
% tfr(256,3)=x(2,1)*x(4,1)=9.37e5
% tfr(1,3)=x(3,1)*x(3,1)=8.5108e5
% tfr(2,3)=x(4,1)*x(2,1)=9.37e5
% tfr(3,3)=x(5,1)*x(1,1)=7.6326e5
% (4)icol=4,第4列, ti=4, taumax=3,tau=-3,-2,-1,0,1,2,3;indices=254,255,256,1,2,3,4
% tfr(254,4)=x(1,1)*x(7,1)=1.0168e6
% tfr(255,4)=x(2,1)*x(6,1)=9.941e5
% tfr(256,4)=x(3,1)*x(5,1)=9.6917e5
% tfr(1,4)=x(4,1)*x(4,1)=1.1375e6
% tfr(2,4)=x(5,1)*x(3,1)=9.6917e5
% tfr(3,4)=x(6,1)*x(2,1)=9.941e5
% tfr(4,4)=x(7,1)*x(1,1)=1.0168e6
% (5)icol=5,第5列, ti=5, taumax=4,tau=-4,-3,-2,-1,0,1,2,3,4;indices=253,254,255,256,1,2,3,4,5
% tfr(253,5)=x(1,1)*x(9,1)=1.0924e6
% tfr(254,5)=x(2,1)*x(8,1)=1.2928e6
% tfr(255,5)=x(3,1)*x(7,1)=1.2911e6
% tfr(256,5)=x(4,1)*x(6,1)=1.2068e6
% tfr(1,5)=x(5,1)*x(5,1)=1.1036e6
% tfr(2,5)=x(6,1)*x(4,1)=1.2068e6
% tfr(3,5)=x(7,1)*x(3,1)=1.2911e6
% tfr(4,5)=x(8,1)*x(2,1)=1.2928e6
% tfr(5,5)=x(9,1)*x(1,1)=1.0924e6
% 第2到128行与256到130行，上下以第129行为轴对应列元素相等，第1行为输入矢量各元素平方项（自身与其共轭相乘），
% 第129行始终为0；横轴方向，即由左到右列向为时间，1到256点（将时间离散点化，此处32ms）；行索引indices与tau有关系，
% 第1行，tau=0；第2行，tau=1；第3行，tau=2；...；第128行，tau=127。
% 下面用fft对1到256行的tau计算傅氏变换
% If 输入 is a matrix, fft returns the Fourier transform of each column of the matrix.

tfr= fft(tfr);                                  % ***  tfr (Nxtcol) 矩阵，行指频点，列指时间  ***
% tfr第2到128行与256到130行，上下以第129行为轴对应列元素相等，第1行与其他行不同，第129行与其他行不同；
% 横轴方向，即由左到右列向为时间，1到256点（将时间离散点化，此处32ms）；
% 可取上半部分第1行，第2行到128行，第129行共129行的129点，与频率范围（0到4000Hz）对应，省掉下半部分256到130行的重复内容。

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

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