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VWdiag3.m
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VWdiag3.m
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% function diag3=VWdiag3(xn, yn, os, R, A, delay, k1)
%
% diag3 is the third order kernel of Wiener series according to our method,
% which will contain not-a-NaN values ony within the set of fundamental
% diagonal points, which is the minimum set of diagonal points which allows
% the reconstruction of diagonal kernel points by symmetry
% (see symmetrize function).
% For non-diagonal points refer to LeeSch3 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(diag3)-1. The lags domain interval
% corresponding to diag3 is [0,R]x[0,R]x[0,R].
%
% A is the second order moment of xn (i.e. power).
%
% 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.
%
% k1 is the previously obtained Wiener kernel of the first order.
%
% If you want to contact the authors, please write to [email protected],
% or Simone Orcioni, DII, Università Politecnica delle Marche,
% via Brecce Bianche, 12 - 60131 Ancona, Italy.
% If you are using this program for a scientific work, we encourage you to cite
% the following paper (the file cite.bib, containing the reference in bibtex
% format is also provided):
%
% Simone Orcioni, Massimiliano Pirani, and Claudio Turchetti. Advances in
% Lee-Schetzen method for Volterra filter identification. Multidimensional
% Systems and Signal Processing, 16(3):265-284, 2005.
%
% Simone Orcioni. Improving the approximation ability of Volterra series
% identified with a cross-correlation method. Nonlinear Dynamics, 2014.
%
%Orcioni, S., Terenzi, A., Cecchi, S., Piazza, F., & Carini, A. (2018).
% Identification of Volterra Models of Tube Audio Devices using
% Multiple-Variance Method. Journal of the Audio Engineering Society,
% 66(10), 823–838. https://doi.org/10.17743/jaes.2018.0046
% Copyright (C) 2006 Massimiliano Pirani
% Copyright (C) 2017 Simone Orcioni
%
% 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 diag3=VWdiag3(xn,yn,os,R,A,delay,k1)
if not(isscalar(delay))
delay3 = delay(2);
delay31 = delay(2)-delay(1);
else
delay3 = delay;
delay31 = delay;
end
diag3=NaNmat(R+1,R+1,R+1);
A3=A*A*A;
for sgm1=0:R
p1=[zeros(sgm1,1);xn(os:end-sgm1-delay3)];
for sgm2=sgm1:R
p2=[zeros(sgm2,1);xn(os:end-sgm2-delay3)];
for sgm3=sgm2:R
if (sgm3~=sgm1) && (sgm3~=sgm2) && (sgm2~=sgm1)
break
else
diag3(sgm3+1,sgm2+1,sgm1+1)=1/6/A3* mean(...
p1.*...
p2.*...
[zeros(sgm3,1);xn(os:end-sgm3-delay3)].*...
yn(os+delay3:end) )...
-1/6/A*( k1(sgm1+1+delay31)*(sgm2==sgm3)+k1(sgm2+1+delay31)*(sgm1==sgm3)+k1(sgm3+1+delay31)*(sgm1==sgm2) );
end
end
end
end