tfrsp.m

时频分析工具箱

function [tfr,t,f] = tfrsp(x,t,N,h,trace);
%TFRSP	Spectrogram time-frequency distribution.
%	[TFR,T,F]=TFRSP(X,T,N,H,TRACE) computes the Spectrogram 
%	distribution of a discrete-time signal X. 
% 
%	X     : signal.
%	T     : time instant(s)          (default : 1:length(X)).
%	N     : number of frequency bins (default : length(X)).
%	H     : analysis 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 representation. When called without 
%	        output arguments, TFRSP runs TFRQVIEW.
%	F     : vector of normalized frequencies.
%
%	Example :
%	 sig=fmlin(128,0.1,0.4);
%	 h=window(17,'Kaiser'); tfrsp(sig,1:128,64,h,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 (nargin < 1),
 error('At least 1 parameter is required');
elseif (nargin <= 2),
 N=xrow;
end;

hlength=floor(N/4);
hlength=hlength+1-rem(hlength,2);

if (nargin == 1),
 t=1:xrow; h = window(hlength); trace=0;
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==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; 

[hrow,hcol]=size(h); Lh=(hrow-1)/2;
if (hcol~=1)|(rem(hrow,2)==0),
 error('H must be a smoothing window with odd length');
end;

tfr= zeros (N,tcol) ;  
if trace, disp('Spectrogram'); end;
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).*conj(h(Lh+1+tau))/norm(h(Lh+1+tau));
end;
%------icol=1,ti=1,tau=0,1,2,3,4,5,6,indices=1,2,3,4,5,6,7----------speech1000          
% tfr(1,1)=x(1).*h(7)/1.8107=-2.1359, tfr(2,1)=x(2).*h(8)/1.8107=-2.4651,tfr(3,1)=x(3).*h(9)/1.8107=-2.2424,
% tfr(4,1)=x(4).*h(10)/1.8107=-2.0141,tfr(5,1)=x(5).*h(11)/1.8107=-1.3516,tfr(6,1)=x(6).*h(12)/1.8107=-0.84225,
% tfr(7,1)=x(7).*h(13)/1.8107=-0.51658
%------icol=2,ti=2,tau=-1,0,1,2,3,4,5,6,indices=256,1,2,3,4,5,6,7
% tfr(256,2)=x(1).*h(6)/2.0468=-1.8034,tfr(1,2)=x(2).*h(7)/2.0468=-2.2848,tfr(2,2)=x(3).*h(8)/2.0468=-2.2899,
% tfr(3,2)=x(4).*h(9)/2.0468=-2.2933,tfr(4,2)=x(5).*h(10)/2.0468=-1.7550,tfr(5,2)=x(6).*h(11)/2.0468=-1.2879,
% tfr(6,2)=x(7).*h(12)/2.0468=-0.9216,tfr(7,2)=x(8).*h(13)/2.0468=-0.4805
% 分析窗h先由正半侧由第1个样值x(1),x(2),x(3),x(4),x(5),x(6),x(7),向最后1个样值x(256)滑行;最后与样值x(250),x(251),
% x(253),x(254),x(255),x(256),对应相乘的窗h(1),h(2),h(3),h(4),h(5),h(6),h(7).

tfr=abs(fft(tfr)).^2;                           % ***  tfr (Nxtcol) 矩阵，行指频点，列指时间  ***
% tfr第1列：
% (1) 133.81
% (2) 133.58
% (3) 132.88
% (4) 131.71
% (5) 130.1
% ...        第1，129行单独成行；第2行到第128行(127行)与第256行到第130行(127行)以第129行为轴上下对应 
% (127)0.83925
% (128)0.85153
% (129)0.85567
% (130)0.85153
% (131)0.83925
% ...       只取第1行到129行可作为，0到4000Hz频率范围
% (253)130.1
% (254)131.71
% (255)132.88
% (256)133.58
if trace, fprintf('\n'); end;
if (nargout==0),
 tfrqview(tfr,x,t,'tfrsp',h);
elseif (nargout==3),
 f=fftshift((-N/2:N/2-1)/N)';
end;