tfrstft.m

时频分析工具箱

function [tfr,t,f] = tfrstft(x,t,N,h,trace);
%TFRSTFT Short time Fourier transform.
%	[TFR,T,F]=TFRSTFT(X,T,N,H,TRACE) computes the short-time Fourier 
%	transform of a discrete-time signal X. 
% 
%	X     : signal.
%	T     : time instant(s)          (default : 1:length(X)).               时间刻度：1:256 
%	N     : number of frequency bins (default : length(X)).                 频率点数：256，N为2的几次幂 
%	H     : frequency smoothing window, H being normalized so as to
%	        be  of unit energy.      (default : Hamming(N/4)). 
%	TRACE : if nonzero, the progression of the algorithm is shown
%	                                 (default : 0).
%	TFR   : time-frequency decomposition (complex values). The
%	        frequency axis is graduated from -0.5 to 0.5.
%	F     : vector of normalized frequencies.
%
%	Example :
%	 sig=[fmconst(128,0.2);fmconst(128,0.4)]; tfr=tfrstft(sig);
%	 subplot(211); imagesc(abs(tfr));
%	 subplot(212); imagesc(angle(tfr));
% 
%	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] 

[xrow,xcol] = size(x);
if (nargin < 1),
 error('At least 1 parameter is required');
elseif (nargin <= 2),
 N=xrow;                                                % For a faster computation, N should be a power of two
end;

hlength=floor(N/4);
hlength=hlength+1-rem(hlength,2);                       % modidy window length so that hlength is odd. 

if (nargin == 1),
 t=1:xrow; h = window(hlength); trace=0;                % 时间点设为输入信号长度
elseif (nargin == 2) | (nargin == 3),
 h = window(hlength); trace = 0;
elseif (nargin == 4),
 trace = 0;
end;

if (N<0),
 error('N must be greater than zero');
end;
[trow,tcol] = size(t);
if (xcol~=1),
 error('X must have one column');
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; 

[hrow,hcol]=size(h); Lh=(hrow-1)/2;                     % get the number of the half window,窗h以列形式保存 
if (hcol~=1)|(rem(hrow,2)==0),
 error('H must be a smoothing window with odd length');
end;

h=h/norm(h);                                            % window energy normalization

tfr= zeros (N,tcol) ;                                   % initialize output time frequency distribution matrix, N:frequency bin axis, tcol:time axis
if trace, disp('Short-time Fourier transform'); end;    % N:频率垂直轴，tcol:时间横轴
for icol=1:tcol,
 ti= t(icol); tau=-min([round(N/2)-1,Lh,ti-1]):min([round(N/2)-1,Lh,xrow-ti]);
 indices= rem(N+tau,N)+1; 
 if trace, disprog(icol,tcol,10); end;
 tfr(indices,icol)=x(ti+tau,1).*conj(h(Lh+1+tau));
end;

% x(ti+tau,1).*conj(h(Lh+1+tau)) 完成加窗。输入信号：xrow,256点（时间）；xrol,1。初始，ti=1,tau=0,1,2...31,32。共取33信号点。
% 窗取Lh=32,h(Lh+1+tau)为右半侧窗，且取共轭。进行x(ti+tau,1)和conj(h(Lh+1+tau))的33点对应相乘。放入tfr占据(1,..,33)x1位置。
% ti向右移一点ti=2,tau=-1,0,...,32。indices：256,1,2,...,33。tfr(indices,icol)占据(256,1,2,...,33)x2的位置。
% ti向右移一点ti=3,tau=-2,-1,...,32。indices：255,256,1,...,33。tfr(indices,icol)占据(255,256,1,2,...,33)x3的位置。
% ti向右移一点ti=4,tau=-3,-2,-1,...,32。indices：254,255,256,1,...,33。tfr(indices,icol)占据(254,255,256,1,2,...,33)x3的位置。
% ti向右移一点ti=5,tau=-4,-3,-2,-1,...,32。indices：253,254,255,256,1,...,33。tfr(indices,icol)占据(253,254,255,256,1,2,...,33)x3的位置。
% ......
% ti向右移ti=32,indices：225,...,256,1,...,33。tfr(indices,icol)占据(225,...,256,1,2,...,33)x32的位置。
% ......
% ti向右移一点ti=128,tau=-32,-31,...,31,32。indices：225,...,256,1,...,33。tfr(indices,icol)占据(225,...,256,1,...,33)x128的位置。
% ......
% ti向右移ti=225,indices：225,...,256,1,...,32。tfr(indices,icol)占据(225,...,256,1,...,32)x225的位置。
% ti向右移ti=256,indices：225,...,256,1。tfr(indices,icol)占据(225,...,256,1)x256的位置。

tfr=fft(tfr);                                           % TFRSTFT Short time Fourier transform,只是fft,并不是功率谱
if trace, fprintf('\n'); end;                           % ***  tfr (Nxtcol矩阵，行和列相等，行指频点，列指时间  ***

if (nargout==0),
 tfrqview(abs(tfr).^2,x,t,'tfrstft',h);
elseif (nargout==3),
 f=fftshift(0.5*(-N:N-1)/N)';
end;