LeeSch3.m

%function [k3]=LeeSch3(xn, yn, os, R, A, swap, delay)
%
% k3 is the third order kernel of Wiener series according to Lee-Schetzen 
% method, which will contain not-a-NaN values ony within the set of 
% fundamental points, which is the minimum set of non-diagonal points which 
% allows the reconstruction of non-diagonal kernel points by symmetry 
% (see symmetrize function).
% For diagonal points refer to WVdiag3 function.
%
% xn is the input sequence, yn the output sequence.
%
% os is the input/output sequences index from where the cross-correlation is
% started, all the sequence values before os are thrown. In can be used when 
% xn and yn have been obtained from an A/D conversion and we the initial 
% transient conditions cut away.
%
% R is the length corresponding to length(k3)-1. The lags domain interval 
% corresponding to k3 is [0,R]x[0,R]x[0,R].
%
% A is the second order moment of xn (i.e. power).
%
% swap is an optional parameter for speed optimization 
% (see fastxcorr for insights),
% it depends on the machine you're on, and on having compiled this code or not.
% If you don't know what to do use default value.
% (We choose 23 in octave environment and 11 in the standalone version)
%
% delay gives the result restricted to the lags domain interval
% [0+delay,R]x[0+delay,R]x[0+delay,R], most useful for higher order kernels.
%
% If you want to contact the authors, please write to s.orcioni@univpm.it,
% or Simone Orcioni, DII, Università Politecnica delle Marche,
% via Brecce Bianche, 12 - 60131 Ancona, Italy.

% Copyright (C) 2006 Massimiliano Pirani
%
%  This program is free software; you can redistribute it and/or modify
%  it under the terms of the GNU General Public License as published by
%  the Free Software Foundation; either version 2 of the License, or
%  (at your option) any later version.
%
%  This program is distributed in the hope that it will be useful,
%  but WITHOUT ANY WARRANTY; without even the implied warranty of
%  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%  GNU General Public License for more details.
%
%  You should have received a copy of the GNU General Public License along
%  with this program; if not, write to the Free Software Foundation, Inc.,
%  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

function [k3]=LeeSch3(xn,yn,os,R,A,swap,delay)
    L=length(xn(os:end-delay));
    A3=A*A*A;
    k3=NaNmat(R+1,R+1,R+1);
    for sgm2=1:R-1
        p2=[zeros(sgm2,1);xn(os:end-sgm2-delay)];
        for sgm1=sgm2+1:R;
            k3(sgm1+1,sgm2+1,1:sgm2)=frxcorr(xn(os:end-delay),...
                p2.*[zeros(sgm1,1);xn(os:end-sgm1-delay)].*yn(os+delay:end),...
                L,...
                sgm2-1,0,swap)/6/A3;
        end
    end 
end