www.pudn.com > TimeFrequency.rar > TFDist_AF.m

function aftf = TFDist_AF(sig) 
% TFDist_AF -- Alias-Free Generalized Discrete Time-Frequency Distribution 
%  Usage 
%    aftf = TFDist_AF(sig) 
%  Inputs 
%    sig     1-d signal of dyadic length n=2^J 
%  Outputs 
%    aftf    complex-valued matrix representing the alias-free generalized 
%            time-frequency distribution of zero-extended signal with rows 
%            corresponding to frequencies and columns corresponding to times 
% 
%  Side Effects 
%    Image Plot of the alias free TF distribution 
% 
%  See Also 
%   WigDist, AFWigDist, specgram, ImagePhasePlane 
% 
%  References 
%   Jechang Jeong and William J. Williams, 
%   "Alias-Free Generalized Discrete-Time Time-Frequency Distribution 
%   IEEE Transactions on Signal Processing", vol. 40, pp. 2757-2765 
%  
 
sig = sig(:); 
n   = length(sig); 
f   = [zeros(n,1); sig; zeros(n,1)]; 
aftf = zeros(n); 
zerosn = zeros(n,1); 
 
for t=1:n, 
  x = zerosn; 
  for k = 0:(n/2-1), 
    % even indices 
    if k == 0, 
      x(2*k+1) = f(n + t) * f(n+t); 
    else 
      ix = (-k):k; 
      tplus    = n + t + k - ix; 
      tminus   = n + t - k - ix; 
      ff = f(tplus) .* f(tminus); 
      b = 1/((2*k+1)*.54 + .46 * ... 
	real((exp(i*2*pi*(k+1)/(2*k))-exp(-i*pi))/ ... 
	(1 - exp(i*pi/k)))); 
      x(2*k+1) = b*(.54+.46*cos(2*pi*ix/(2*k))) * ff; 
    end 
     
    % odd indices 
    ix = (-k):(k+1); 
    tplus = n + t + k - ix + 1; 
    tminus   = n + t - k - ix; 
    ff = f(tplus) .* f(tminus); 
    b = 1/((2*k+2)*.54 + .46 * ... 
      real((exp(i*2*pi*(k+2)/(2*k+1)) ... 
      -exp(-i*2*pi*k/(2*k+1))) * exp(-i*pi/(2*k+1))/ ... 
      (1 - exp(i*2*pi/(2*k+1))))); 
    x(2*k+2) = b*(.54+.46*cos(2*pi*(ix-.5)/(2*k+1)))*ff; 
  end 
%  aftf(:,t) = 2 * real(fft(x)); 
  aftf(:,t) = 2 * real(fftshift(fft(x))); 
end 
 
% abstf = abs(aftf); 
abstf = aftf; 
tfmax = max(max(abstf)); 
tfmin = min(min(abstf)); 
colormap(1-gray(256)) 
image(linspace(0,1,n),linspace(0,1,n),256*(abstf-tfmin)/(tfmax-tfmin)); 
axis('xy') 
title('Alias Free Time-Frequency Distribution'); 
xlabel('Time') 
ylabel('Frequency') 
 
% 
% Copyright (c) 1994-5, Shaobing Chen 
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% Part of WaveLab Version 802 
% Built Sunday, October 3, 1999 8:52:27 AM 
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