tfrridbn.m

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function [tfr,t,f] = tfrridbn(x,t,N,g,h,trace);
%TFRRIDBN Reduced Interference Distribution with a binomial kernel.
%       [TFR,T,F]=TFRRIDBN(X,T,N,G,H,TRACE) Reduced Interference
%       Distribution with a kernel based on the binomial coefficients.
%       TFRRIDBN computes either the distribution of a discrete-time 
%       signal X, or the cross representation between two signals. 
% 
%       X     : signal if auto-RIDBN, or [X1,X2] if cross-RIDBN.
%       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)). 
%       TRACE : if nonzero, the progression of the algorithm is shown
%                                        (default : 0).
%       TFR   : time-frequency representation. When called without 
%               output arguments, TFRRIDBN runs TFRQVIEW.
%       F     : vector of normalized frequencies.
%
%       Example :
%        sig=[fmlin(128,.05,.3)+fmlin(128,.15,.4)]; tfrridbn(sig); 
% 
%       See also all the time-frequency representations listed in
%        the file CONTENTS (TFR*)

%       F. Auger, June 1996.
%       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 & nargin==6),
 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 = window(glength); h = window(hlength); trace = 0;
elseif (nargin == 2)|(nargin == 3),
 g = window(glength); h = window(hlength); trace = 0;
elseif (nargin == 4),
 h = window(hlength); trace = 0;
elseif (nargin == 5),
 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; g=g/g(Lg+1);
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;

taumax = min([round(N/2)-1,Lh]);

tfr= zeros (N,tcol) ;  
if trace, disp('Binomial RID 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)= g(Lg+1) * x(ti,1) .* conj(x(ti,xcol));

 Ker=[1];
 for tau=1:taumax,
  points= -min([tau,Lg,xrow-ti-tau]):min([tau,Lg,ti-tau-1]);
  Ker= ([Ker; 0; 0]+2*[0; Ker; 0]+[0; 0; Ker])/4.0; 
  g2 = g(Lg+1+points) .* Ker(tau+points+1); 
  if (sum(g2)>eps), g2=g2/sum(g2); end;
  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),
  Ker=ones(2*tau+1,1);
  for p=1:2*tau,
   Ker(p+1)=Ker(p)*(2*tau-p+1)/p;
  end;
  Ker=Ker/sum(Ker);
  points= -min([tau,Lg,xrow-ti-tau]):min([tau,Lg,ti-tau-1]);
  g2 = g(Lg+1+points) .* Ker(tau+points+1); 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; 

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

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