Wiener2Volterra_20.m

% function [h0,h1,h2,...,hp]=Wiener2Volterra(A, k0, k1, k2, k3, k4, k5)
%
% Volterra kernels h0,h1,h2,...,h5 are obtained from Wiener kernels.
% A is a vector of the power of the zero-mean white gaussian input used
% for Wiener identification of different order kernels.
% See Documentation and References provided.
%
% 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.
% 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. 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 varargout=Wiener2Volterra_20(delays,A,k0,k1,k2,k3,k4,k5)

if exist('k1','var')
    if size(k1,1)==1,k1=k1';end
end


switch nargin
case 3 % zero 
    varargout{1}=k0;
    
case 4 % first order
    varargout{1}=k0;
    varargout{2}=k1;
    
case 5 % second order
        
    varargout{1}=k0+k02f(k2,A(1));
    varargout{2}=k1;
    varargout{3}=k2;
    
case 6 % third order
    
    R1=size(k1,1);
    R3=size(k3,1);
    varargout{1}=k0+k02f(k2,A(1));
    varargout{2}=[k1;zeros(R3-R1,1)]+[zeros(delays(3),1);k13f(k3,A(2));zeros(R1-R3-delays(3),1)];%h1
    varargout{3}=k2;%h2
    varargout{4}=k3;%h3

case 7 % fourth order
    
    R1=size(k1,1);
    R2=size(k2,1);
    R3=size(k3,1);
    R4=size(k4,1);
    
    varargout{1}=k0+k02f(k2,A(1))+k04f(k4,A(1));%h0
    varargout{2}=[k1;zeros(R3-R1,1)]+[zeros(delays(3),1);k13f(k3,A(2));zeros(R1-R3-delays(3),1)];%h1
    kz=zeros(max([R4,R2]));
    kz(1:R2,1:R2)=k2;k2=kz;
    kz=zeros(max([R4,R2]));
    k24=k24f(k4,A(3));
    kz(1+delays(4)-delays(2):R4+delays(4)-delays(2),1+delays(4)-delays(2):R4+delays(4)-delays(2))=k24;k24=kz;
    varargout{3}=k2+k24;%h2
    varargout{4}=k3;%h3
    varargout{5}=k4;%h4

    
case 8 % fifth order
    
    R1=size(k1,1);
    R2=size(k2,1);
    R3=size(k3,1);
    R4=size(k4,1);
    R5=size(k5,1);
    
    R135=max([R1,R3,R5]);
    R24=max([R2,R4]);
    R35=max([R3,R5]);
    
    varargout{1}=k0+k02f(k2,A(1))+k04f(k4,A(1));%h0
    varargout{2}=[k1;zeros(R135-R1,1)]+[k13f(k3,A(2));zeros(R135-R3,1)]+[k15f(k5,A(2));zeros(R135-R5,1)];%h1
    kz=zeros(R24);
    kz(1:R2,1:R2)=k2;k2=kz;
    kz=zeros(R24);
    k24=k24f(k4,A(3));
    kz(1:R4,1:R4)=k24;k24=kz;
    varargout{3}=k2+k24;%h2
    kz=zeros(R35,R35,R35);
    kz(1:R3,1:R3,1:R3)=k3;k3=kz;
    k35=k35f(k5,A(4));
    kz=zeros(R35,R35,R35);
    kz(1:R5,1:R5,1:R5)=k35;k35=kz;
    varargout{4}=k3+k35;%h3
    varargout{5}=k4;%h4
    varargout{6}=k5;%h5
    
otherwise
    error('input parameter number is not valid');
end