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function [Bspec,waxis] = bispecd (y, nfft, wind, nsamp, overlap)
%BISPECD Bispectrum estimation using the direct (fft-based) approach.
% [Bspec,waxis] = bispecd (y, nfft, wind, segsamp, overlap)
% y - data vector or time-series
% nfft - fft length [default = power of two > segsamp]
% wind - window specification for frequency-domain smoothing
% if 'wind' is a scalar, it specifies the length of the side
% of the square for the Rao-Gabr optimal window [default=5]
% if 'wind' is a vector, a 2D window will be calculated via
% w2(i,j) = wind(i) * wind(j) * wind(i+j)
% if 'wind' is a matrix, it specifies the 2-D filter directly
% segsamp - samples per segment [default: such that we have 8 segments]
% - if y is a matrix, segsamp is set to the number of rows
% overlap - percentage overlap [default = 50]
% - if y is a matrix, overlap is set to 0.
%
% Bspec - estimated bispectrum: an nfft x nfft array, with origin
% at the center, and axes pointing down and to the right.
% waxis - vector of frequencies associated with the rows and columns
% of Bspec; sampling frequency is assumed to be 1.
% Copyright (c) 1991-2001 by United Signals & Systems, Inc.
% $Revision: 1.8 $
% A. Swami January 20, 1993.
% RESTRICTED RIGHTS LEGEND
% Use, duplication, or disclosure by the Government is subject to
% restrictions as set forth in subparagraph (c) (1) (ii) of the
% Rights in Technical Data and Computer Software clause of DFARS
% 252.227-7013.
% Manufacturer: United Signals & Systems, Inc., P.O. Box 2374,
% Culver City, California 90231.
%
% This material may be reproduced by or for the U.S. Government pursuant
% to the copyright license under the clause at DFARS 252.227-7013.
% --------------------- parameter checks -----------------------------
[ly, nrecs] = size(y);
if (ly == 1) y = y(:); ly = nrecs; nrecs = 1; end
if (exist('nfft') ~= 1) nfft = 128; end
if (exist('overlap') ~= 1) overlap = 50; end
overlap = min(99,max(overlap,0));
if (nrecs > 1) overlap = 0; end
if (exist('nsamp') ~= 1) nsamp = 0; end
if (nrecs > 1) nsamp = ly; end
if (nrecs == 1 & nsamp <= 0)
nsamp = fix(ly/ (8 - 7 * overlap/100));
end
if (nfft < nsamp) nfft = 2^nextpow2(nsamp); end
overlap = fix(nsamp * overlap / 100); % added 2/14
nadvance = nsamp - overlap;
nrecs = fix ( (ly*nrecs - overlap) / nadvance);
% ------------------- create the 2-D window -------------------------
if (exist('wind') ~= 1) wind = 5; end
[m,n] = size(wind);
window = wind;
if (max(m,n) == 1) % scalar: wind is size of Rao-Gabr window
winsize = wind;
if (winsize < 0) winsize = 5; end % the window length L
winsize = winsize - rem(winsize,2) + 1; % make it odd
if (winsize > 1)
mwind = fix (nfft/winsize); % the scale parameter M
lby2 = (winsize - 1)/2;
theta = -lby2:lby2;
opwind = ones(winsize,1) * (theta .^2); % w(m,n)=m^2
opwind = opwind + opwind' + theta' * theta; % m^2 + n^2 + mn
opwind = 1 - (2*mwind/nfft)^2 * opwind; %
hex = ones(winsize,1) * theta; % m
hex = abs(hex) + abs(hex') + abs(hex+hex');
hex = (hex < winsize);
opwind = opwind .* hex;
opwind = opwind * (4 * mwind^2) / (7 * pi^2) ;
else
opwind = 1;
end
elseif (min(m,n) == 1) % 1-D window passed: convert to 2-D
window = window(:);
if (any(imag(window) ~= 0))
disp(['1-D window has imaginary components: window ignored'])
window = 1;
end
if (any(window < 0))
disp(['1-D window has negative components: window ignored'])
window = 1;
end
lwind = length(window);
windf = [window(lwind:-1:2); window]; % the full symmetric 1-D
window = [window; zeros(lwind-1,1)];
opwind = (windf * windf') ...
.* hankel(flipud(window), window); % w(m)w(n)w(m+n)
winsize = length(window);
else % 2-D window passed: use directly
winsize = m;
if (m ~= n)
disp('2-D window is not square: window ignored')
window = 1;
winsize = m;
end
if (rem(m,2) == 0)
disp('2-D window does not have odd length: window ignored')
window = 1;
winsize = m;
end
opwind = window;
end
% ---------------- accumulate triple products ----------------------
Bspec = zeros(nfft,nfft);
mask = hankel([1:nfft],[nfft,1:nfft-1] ); % the hankel mask (faster)
locseg = [1:nsamp]';
for krec = 1:nrecs
xseg = y(locseg);
Xf = fft(xseg-mean(xseg), nfft)/nsamp;
CXf = conj(Xf);
Bspec = Bspec + (Xf * Xf.') .* ...
reshape(CXf(mask), nfft, nfft);
locseg = locseg + nadvance;
end
Bspec = fftshift(Bspec)/(nrecs);
% ----------------- frequency-domain smoothing ------------------------
if (winsize > 1)
lby2 = (winsize-1)/2;
Bspec = conv2(Bspec,opwind);
Bspec = Bspec(lby2+1:lby2+nfft,lby2+1:lby2+nfft);
end
% ------------ contour plot of magnitude bispectum --------------------
if (rem(nfft,2) == 0)
waxis = [-nfft/2:(nfft/2-1)]'/nfft;
else
waxis = [-(nfft-1)/2:(nfft-1)/2]'/nfft;
end
hold off, clf
% contour(abs(Bspec),4,waxis,waxis),grid
contour(waxis,waxis,abs(Bspec),4),grid on
title('Bispectrum estimated via the direct (FFT) method')
xlabel('f1'), ylabel('f2')
set(gcf,'Name','Hosa BISPECD')
return