d_bispd.m

完整的高阶谱工具箱和说明文档

%D_BISPD  HOSA Demo: Direct estimate of the bispectrum (bispecd)
%       

echo off 
% A. Swami Oct 18, 1997.
% Copyright (c) 1991-2001 by United Signals & Systems, Inc. 
%       $Revision: 1.6 $

%     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. 

clear, clc, 

echo on 
%
%    BISPECD : bispectrum estimation using the direct method.
%
% Here, the given time-series, x(n), is segmented into several, possibly
% over-lapping, records,  xi(n), i=1, ..., K,  n=1, ... , M. 
% The Fourier transform of each record is computed, Xi(f). 
% The sample triple product is computed, Xi(f1) Xi(f2) conj(Xi(f1+f2)), 
% and averaged across the set of records,
%
%   1/MK sum {over i} Xi(f1) Xi(f2) conj( Xi(f1+f2) ) 
%
% A frequency-domain smoothing window is then applied to obtain the
% final estimate. 
%
% Hit any key to continue 
pause
%
% The data for the demo is a synthetic for the quadratic-phase coupling (QPC)
% problem, and consist of four unity amplitude harmonics with frequencies
% 0.1 Hz, 0.15 Hz, 0.25 Hz and 0.40 Hz.  64 independent realizations, each 
% consisting of 64 samples, were generated using routine QPCGEN. The starting 
% phases for the harmonics with frequencies, 0.1 Hz, 0.15 Hz and 0.40 Hz were 
% chosen independently from an uniform distribution; the starting phase of the
% third harmonic, at 0.25 Hz, was set equal to the the sum of the starting 
% phases of the harmonics at 0.1 Hz and 0.15 Hz. White Gaussian noise with a
% variance of 1.5 was added to the signal.  Note that the harmonics at 
% (0.1, 0.15, 0.25) are both frequency- and phase-coupled; whereas those at 
% (0.15, 0.25, 0.40) are frequency-coupled, but not phase-coupled.  

load qpc
% We will use BISPECD with an FFT length of 128 and window length of 3. 
% A contour plot of the bispectrum magnitude will be displayed.
%
% Hit any key to continue 
pause

clf
[bd,w] = bispecd(zmat,128,3,64,0); 
set (gcf, 'Name','HOSA - BISPECD')

% The contour plot shows a shark peak at (f1,f2) = (0.10,0.15);  the 
% other 11 peaks are due to the symmetry properties of the bispectrum.
% In general, we need to concentrate only on the region 0 <= f1 <= f2. 
% The sharpness of the contour peaks indicates the presence of quadratic 
% phase-coupling.   

% Hit any key to return to the previous menu 
pause 
echo off 
clc