FUNCIONES BIOMEDICAS5.rar_biomedical_biomedical signal

%LTI_INT Integrate LTI ODE with Gaussian Noise % % Syntax: % [x,P,A] = lti_int(x,P,F,L,Q,T) % % Description: % Integrates LTI differential equation % % x' = F*x + L*w , w ~ N(0,Q) % % from t0=0 to t1=T or over given steps t0,t1,t2,t3,... % Initial conditions can be in form % % x(t0) = x0 % % or % % x(t0) ~ N(x0,P0) % % See also % LTI_DISC % History: % 20.11.2002 The first official version. % % Copyright (C) 2002 Simo S�rkk� % % $Id: lti_int.m 111 2007-09-04 12:09:23Z ssarkka $ % % This software is distributed under the GNU General Public % Licence (version 2 or later); please refer to the file % Licence.txt, included with the software, for details. function [x,P,A] = lti_int(x,P,F,L,Q,T) % % Check number of arguments % if nargin < 3 error('Too few arguments'); end if nargin < 4 L = []; end if nargin < 5 Q = []; end if nargin < 6 T = []; end % % Integrate one or many steps % if length(T) > 1 % % Handle multiple time steps recursively % if isempty(P) if isempty(x) % % No x or P given, return only A's % tA = eye(size(x,1)); A = zeros(size(x,1),size(x,1),length(T)); A(:,:,1) = tA; for i=2:length(T) [tx,tP,tA] = lti_int([],[],F,L,Q,T(i)-T(i-1)); A(:,:,i) = tA; end else % % Only x given, returns x's and A's % tx = x; tA = eye(size(x,1)); x = zeros(size(x,1),length(T)); A = zeros(size(x,1),size(x,1),length(T)); x(:,1) = tx; A(:,:,1) = tA; for i=2:length(T) [tx,tP,tA] = lti_int(tx,[],F,L,Q,T(i)-T(i-1)); x(:,i) = tx; A(:,:,i) = tA; end end else % % Both x and P given, return all % tx = x; tP = P; tA = eye(size(x,1)); x = zeros(size(x,1),length(T)); P = zeros(size(x,1),size(x,1),length(T)); A = zeros(size(x,1),size(x,1),length(T)); x(:,1) = tx; P(:,:,1) = tP; A(:,:,1) = tA; for i=2:length(T) [tx,tP,tA] = lti_int(tx,tP,F,L,Q,T(i)-T(i-1)); x(:,i) = tx; P(:,:,i) = tP; A(:,:,i) = tA; end end else % % One step integration from 0 to T % if isempty(L) L = eye(size(x,1)); end if isempty(Q) Q = zeros(size(x,1),size(x,1)); end if isempty(T) T = 1; end % % Closed form integration of mean % A = expm(F*T); x = A*x; % % Runge-Kutta Integration of Covariance % if ~isempty(P) & (nargout > 1) f = inline('F*P+P*F''+L*Q*L','P','t','F','L','Q'); P = rk(f,P,0,T,F,L,Q); end end