function afwig = WVDist_AF(sig)% WVDist_AF -- Alias-Free Wigner-Ville Distribution%  Usage%    afwig = WVDist_AF(sig)%  Inputs%    sig     1-d signal%  Outputs%    afwig   complex-valued matrix representing the alias-free%            Wigner-Ville distribution of zero-extended signal with%            rows corresponding to frequencies and columns corresponding%            to times.%%  Side Effects%    Image Plot of the alias-free Wigner-Ville distribution%%  See Also%    WVDist, WVDist_AF, 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)];afwig = zeros(n, n);ix  = 0:(n/2-1);zerosn = zeros(n,1);for t=1:n,    tplus    = n + t + ix;    tminus   = n + t - ix;    x = zerosn;    %even indices    x(1:2:(n)) = f(tplus) .* f(tminus);    %odd indices    x(2:2:(n)) = (f(tplus+1).*f(tminus) + f(tplus).*f(tminus-1))/2;    temp = 2* (fft(x));    lgh2 = length(temp)/2;    afwig(1:lgh2, t) = temp(1:lgh2);endtemp2 = afwig;clear afwig;afwig = temp2(1:lgh2,:); abstf = abs(afwig);tfmax = max(max(abstf));tfmin = min(min(abstf));colormap(1-gray(256))imagesc(0:.001:.10, 0:1000:5000, log10(abs(afwig)));axis('xy')%image(linspace(0,1,n/2),linspace(0,1,n/2),256*(abstf-tfmin)/(tfmax-tfmin));%image(linspace(0,1,n),linspace(0,1,n),256*(abstf-tfmin)/(tfmax-tfmin));axis('xy')title('Alias Free Wigner Distribution');xlabel('Time')ylabel('Frequency')%% Copyright (c) 1994-5, Shaobing Chen%        %   % Part of WaveLab Version .701% Built Tuesday, January 30, 1996 8:25:59 PM% This is Copyrighted Material% For Copying permissions see COPYING.m% Comments? e-mail wavelab@playfair.stanford.edu%