1 function [MX,PE,arg3] = lattice(Y,lc,Mode);
2 % Estimates AR(p) model parameter with lattice algorithm (Burg 1968)
3 % for multiple channels.
4 % If you have the NaN-tools, LATTICE.M can handle missing values (NaN),
6 % [...] = lattice(y [,Pmax [,Mode]]);
8 % [AR,RC,PE] = lattice(...);
9 % [MX,PE] = lattice(...);
12 % y signal (one per row), can contain missing values (encoded as NaN)
13 % Pmax max. model order (default size(y,2)-1))
14 % Mode 'BURG' (default) Burg algorithm
15 % 'GEOL' geometric lattice
18 % AR autoregressive model parameter
19 % RC reflection coefficients (= -PARCOR coefficients)
20 % PE remaining error variance
21 % MX transformation matrix between ARP and RC (Attention: needs O(p^2) memory)
22 % AR(:,K) = MX(:, K*(K-1)/2+(1:K)); = MX(:,sum(1:K-1)+(1:K));
23 % RC(:,K) = MX(:,cumsum(1:K)); = MX(:,(1:K).*(2:K+1)/2);
25 % All input and output parameters are organized in rows, one row
26 % corresponds to the parameters of one channel
28 % see also ACOVF ACORF AR2RC RC2AR DURLEV SUMSKIPNAN
31 % J.P. Burg, "Maximum Entropy Spectral Analysis" Proc. 37th Meeting of the Society of Exp. Geophysiscists, Oklahoma City, OK 1967
32 % J.P. Burg, "Maximum Entropy Spectral Analysis" PhD-thesis, Dept. of Geophysics, Stanford University, Stanford, CA. 1975.
33 % P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
34 % S. Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
35 % M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
36 % W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
38 % $Id: lattice.m 7687 2010-09-08 18:39:23Z schloegl $
39 % Copyright (C) 1996-2002,2008,2010 by Alois Schloegl <a.schloegl@ieee.org>
40 % This is part of the TSA-toolbox. See also
41 % http://biosig-consulting.com/matlab/tsa/
43 % This program is free software: you can redistribute it and/or modify
44 % it under the terms of the GNU General Public License as published by
45 % the Free Software Foundation, either version 3 of the License, or
46 % (at your option) any later version.
48 % This program is distributed in the hope that it will be useful,
49 % but WITHOUT ANY WARRANTY; without even the implied warranty of
50 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
51 % GNU General Public License for more details.
53 % You should have received a copy of the GNU General Public License
54 % along with this program. If not, see <http://www.gnu.org/licenses/>.
57 if nargin<3, Mode='BURG';
58 else Mode=upper(Mode(1:4));end;
59 BURG=~strcmp(Mode,'GEOL');
63 if nargin<2, lc=N-1; end;
66 [DEN,nn] = sumskipnan((Y.*Y),2);
67 PE = [DEN./nn,zeros(lr,lc)];
69 if nargout<3 % needs O(p^2) memory
70 MX = zeros(lr,lc*(lc+1)/2);
73 % Durbin-Levinson Algorithm
75 [TMP,nn] = sumskipnan(F(:,K+1:N).*B(:,1:N-K),2);
76 MX(:,idx+K) = TMP./DEN; %Burg
77 if K>1, %for compatibility with OCTAVE 2.0.13
78 MX(:,idx+(1:K-1))=MX(:,(K-2)*(K-1)/2+(1:K-1))-MX(:,(idx+K)*ones(K-1,1)).*MX(:,(K-2)*(K-1)/2+(K-1:-1:1));
81 tmp = F(:,K+1:N) - MX(:,(idx+K)*ones(1,N-K)).*B(:,1:N-K);
82 B(:,1:N-K) = B(:,1:N-K) - MX(:,(idx+K)*ones(1,N-K)).*F(:,K+1:N);
85 [PE(:,K+1),nn] = sumskipnan([F(:,K+1:N).^2,B(:,1:N-K).^2],2);
87 [f,nf] = sumskipnan(F(:,K+1:N).^2,2);
88 [b,nb] = sumskipnan(B(:,1:N-K).^2,2);
94 PE(:,K+1) = PE(:,K+1)./nn; % estimate of covariance
96 else % needs O(p) memory
99 % Durbin-Levinson Algorithm
101 [TMP,nn] = sumskipnan(F(:,K+1:N).*B(:,1:N-K),2);
102 arp(:,K) = TMP./DEN; %Burg
104 if K>1, % for compatibility with OCTAVE 2.0.13
105 arp(:,1:K-1) = arp(:,1:K-1) - arp(:,K*ones(K-1,1)).*arp(:,K-1:-1:1);
108 tmp = F(:,K+1:N) - rc(:,K*ones(1,N-K)).*B(:,1:N-K);
109 B(:,1:N-K) = B(:,1:N-K) - rc(:,K*ones(1,N-K)).*F(:,K+1:N);
112 [PE(:,K+1),nn] = sumskipnan([F(:,K+1:N).^2,B(:,1:N-K).^2],2);
114 [f,nf] = sumskipnan(F(:,K+1:N).^2,2);
115 [b,nb] = sumskipnan(B(:,1:N-K).^2,2);
120 PE(:,K+1) = PE(:,K+1)./nn; % estimate of covariance
122 % assign output arguments