# ITE / code / IPA / demos / demo_ARX_IPA.m

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 `%function [] = demo_ARX_IPA() %ARX-IPA (ARX = AutoRegressive with eXogenous input, IPA = Independent Process Analysis) illustration. % %Model: % s(t+1) = \sum_{i=0}^{Ls-1} F_i s(t-i)+\sum_{j=0}^{Lu-1} B_j u(t+1-j)+e(t+1), % x(t) = As(t), %or in short % F[z]s = B[z]u+e, F[z] = I - \sum_{i=0}^{Ls-1} F_i z^{i+1}:stable, B[z] = \sum_{j=0}^{Lu-1} B_j z^j, e:ISA source (see 'demo_ISA.m'), % x = As, A: invertible. %Task: x,u -> A (or W=A^{-1}),s,F[z],B[z],e. % %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu") % %This file is part of the ITE (Information Theoretical Estimators) Matlab/Octave toolbox. % %ITE 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 3 of the License, or (at your option) any later version. % %This software 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 ITE. If not, see . %clear start: clear all; close all; %parameters: %dataset: %driving noise(e): data_type = 'Aw';%see 'sample_subspaces.m' num_of_comps = 3;%number of components/subspaces in sampling %hidden source(s): num_of_samples = 1*1000;%number of samples Ls = 1; %F_0,..._F_{Ls-1},Ls=number of F_i-s; >=1 Lu = 1; %B_0,...,B_{Lu-1},Lu=number of B_j-s; >=1 F_lambda = 0.7; %AR stability parameter, 0