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From: Alois Schloegl <schloegl@us...>  20060303 20:30:59

Update of /cvsroot/octave/octaveforge/extra/tsa In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv20317 Modified Files: mvar.m Log Message: rename NutallStrand to VieiraMorf; fix NutallStrand (mode 3 and 7); update documentation Index: mvar.m =================================================================== RCS file: /cvsroot/octave/octaveforge/extra/tsa/mvar.m,v retrieving revision 1.15 retrieving revision 1.16 diff u d r1.15 r1.16  mvar.m 17 Dec 2005 22:18:35 0000 1.15 +++ mvar.m 3 Mar 2006 20:30:43 0000 1.16 @@ 19,43 +19,26 @@ % All input and output parameters are organized in columns, one column % corresponds to the parameters of one channel. % % Mode determines estimation algorithm. % 0: multichannel LevinsonDurbin Recursion % 1: multichannel Levinson algorithm with correlation function estimation method % also called the "multichannel YuleWalker" using the biased correlation function % 2: [default] NuttallStrand Method [2,5,6,7], % Covariances are normalized by N=length(X)p (unbiased estimates) % also called multichannel Burg algorithm % Yields best estimates according to [1] % 3,7: multichannel Levinsion algorithm [2] using VieiraMorf Method % 4: algorihtm according to [8]  not functional. % 5: NuttallStrand Method [2,5,6,7] % Covariances are normalized by N=length(X) (biased estimates) +% Mode determines estimation algorithm. +% 1: Correlation Function Estimation method using biased correlation function estimation method +% also called the "multichannel YuleWalker" [1,2] +% 6: Correlation Function Estimation method using unbiased correlation function estimation method +% +% 2: Partial Correlation Estimation: VieiraMorf [2] using unbiased covariance estimates. +% In [1] this mode was used and (incorrectly) denominated as NutallStrand. +% Its the DEFAULT mode; according to [1] it provides the most accurate estimates. +% 5: Partial Correlation Estimation: VieiraMorf [2] using biased covariance estimates. % Yields similar results than Mode=2; % 6: multichannel Levinson algorithm with correlation function estimation method % also called the "multichannel YuleWalker" using an unbiased correlation function +% +% 3: Partial Correlation Estimation: NutallStrand [2] (biased correlation function) +% 7: Partial Correlation Estimation: NutallStrand [2] (unbiased correlation function) +% % % REFERENCES: % [1] A. Schloegl, Comparison of Multivariate Autoregressive Estimators. % Signal processing, Elsevier B.V. (in press). +% [1] A. Schl\"ogl, Comparison of Multivariate Autoregressive Estimators. +% Signal processing, Elsevier B.V. (in press). +% available at http://dx.doi.org/doi:10.1016/j.sigpro.2005.11.007 % [2] S.L. Marple "Digital Spectral Analysis with Applications" Prentice Hall, 1987. % [3] M. Kaminski, M. Ding, W. Truccolo, S.L. Bressler, Evaluating causal realations in neural systems: % Granger causality, directed transfer functions and statistical assessment of significance. % Biol. Cybern., 85,145157 (2001) % [4] T. Schneider and A. Neumaier, A. 2001. % Algorithm 808: ARFITa Matlab package for the estimation of parameters and eigenmodes % of multivariate autoregressive models. ACMTransactions on Mathematical Software. 27, (Mar.), 5865. % [5] O.N. Strand, % Multichannel complex maximum entropy (autoregressive) spectral Analysis, % IEEE Trans. Autom. Control, Vol. 22, Aug. 1977, pp. 634640. % [6] A.H. Nuttall, % FORTRAN Program for multivariate linear predictive spectral analysis, employing forward and backward averaging, % Naval Underwater Systems Center Technical Report 5419, New London, Conn. 1976a. % [7] A.H. Nuttall, % Multivariate linear predictive spectral analysis employing weighted forward and backward averaging: % a generalization of Burg's algorithm, % Naval Underwater Systems Center Technical Report 5501, New London, Conn. , 1976b. % [8] M.S. Kay "Modern Spectral Estimation" Prentice Hall, 1988. % % % A multivariate inverse filter can be realized with @@ 109,9 +92,8 @@ [C(:,1:M),n] = covm(Y,'M'); PE(:,1:M) = C(:,1:M)./n; if Mode==0; % %%%%% multichannel Levinsion algorithm [2]  % multivariate Autoregressive parameter estimation  fprintf('Warning MDURLEV: It''s not recommended to use this mode\n') +if Mode==0; % this method is broken + fprintf('Warning MVAR: Mode=0 is broken.\n') C(:,1:M) = C(:,1:M)/N; F = Y; B = Y; @@ 140,12 +122,10 @@ PEB = [eye(M)  ARB(:,K*M+(1M:0))*ARF(:,K*M+(1M:0))]*PEB; PE(:,K*M+(1:M)) = PEF; end; + elseif Mode==1,  %%%%% multichannel Levinson algorithm  %%%%% with correlation function estimation method  %%%%% also called the "multichannel YuleWalker"  %%%%% using the biased correlation +elseif Mode==1, %%%%% LevinsonWiggensRobinson (LWR) algorithm using biased correlation function + % ===== In [1,2] this algorithm is denoted "Multichannel YuleWalker" ===== % C(:,1:M) = C(:,1:M)/N; PEF = C(:,1:M); PEB = C(:,1:M); @@ 164,9 +144,6 @@ tmp = ARF(:,L*M+(1M:0))  ARF(:,K*M+(1M:0))*ARB(:,(KL)*M+(1M:0)); ARB(:,(KL)*M+(1M:0)) = ARB(:,(KL)*M+(1M:0))  ARB(:,K*M+(1M:0))*ARF(:,L*M+(1M:0)); ARF(:,L*M+(1M:0)) = tmp;  %tmp = ARF{L}  ARF{K}*ARB{KL};  %ARB{KL} = ARB{KL}  ARB{K}*ARF{L};  %ARF{L} = tmp; end; RCF(:,K*M+(1M:0)) = ARF(:,K*M+(1M:0)); @@ 176,18 +153,14 @@ PEB = [eye(M)  ARB(:,K*M+(1M:0))*ARF(:,K*M+(1M:0))]*PEB; PE(:,K*M+(1:M)) = PEF; end; + elseif Mode==6,  %%%%% multichannel Levinson algorithm  %%%%% with correlation function estimation method  %%%%% also called the "multichannel YuleWalker"  %%%%% using the unbiased correlation  +elseif Mode==6, %%%%% LevinsonWiggensRobinson (LWR) algorithm using unbiased correlation function C(:,1:M) = C(:,1:M)/N; PEF = C(:,1:M); PEB = C(:,1:M);  for K=1:Pmax, + for K = 1:Pmax, [C(:,K*M+(1:M)),n] = covm(Y(K+1:N,:),Y(1:NK,:),'M'); C(:,K*M+(1:M)) = C(:,K*M+(1:M))./n; %C{K+1} = C{K+1}/N; @@ 212,16 +185,15 @@ PE(:,K*M+(1:M)) = PEF; end; elseif Mode==2,  %%%%% multichannel Burg algorithm  %%%%% using NuttallStrand Method [2,5,6,7]  %%%%% Covariance matrix is normalized by N=length(X)p + +elseif Mode==2 %%%%% Partial Correlation Estimation: VieiraMorf Method [2] with unbiased covariance estimation + %===== In [1] this algorithm is denoted "NutallStrand with unbiased covariance" =====% C(:,1:M) = C(:,1:M)/N; F = Y; B = Y; PEF = C(:,1:M); PEB = C(:,1:M);  for K=1:Pmax, + for K = 1:Pmax, [D,n] = covm(F(K+1:N,:),B(1:NK,:),'M'); D = D./n; @@ 250,11 +222,9 @@ PE(:,K*M+(1:M)) = PEF; end; elseif Mode==5,  %%%%% multichannel Burg algorithm  %%%%% using NutallStrand Method [2,5,6,7]  %%%%% Covariance matrix is normalized by N=length(X)  + +elseif Mode==5 %%%%% Partial Correlation Estimation: VieiraMorf Method [2] with biased covariance estimation + %===== In [1] this algorithm is denoted "NutallStrand with biased covariance" ===== % %C{1} = C{1}/N; F = Y; B = Y; @@ 288,9 +258,9 @@ PE(:,K*M+(1:M)) = PEF; end; + elseif Mode==3, %%%%% multichannel Levinsion algorithm [2] using VieiraMorf Method  fprintf('Warning MDURLEV: It''s not recommended to use this mode\n') +elseif Mode==3 %%%%% Partial Correlation Estimation: NutallStrand Method [2] with biased covariance estimation C(:,1:M) = C(:,1:M)/N; F = Y; B = Y; @@ 298,10 +268,10 @@ PEB = C(:,1:M); for K=1:Pmax, [D, n] = covm(F(K+1:N,:),B(1:NK,:),'M');  D = D./n; + D = D./N;  ARF(:,K*M+(1M:0)) = (PEF.^.5)*D*(PEB.^.5)';  ARB(:,K*M+(1M:0)) = ARF(:,K*M+(1M:0)); + ARF(:,K*M+(1M:0)) = 2*D / (PEB+PEF); + ARB(:,K*M+(1M:0)) = 2*D'/ (PEF+PEB); tmp = F(K+1:N,:)  B(1:NK,:)*ARF(:,K*M+(1M:0)).'; B(1:NK,:) = B(1:NK,:)  F(K+1:N,:)*ARB(:,K*M+(1M:0)).'; @@ 317,17 +287,17 @@ RCF = ARF(:,K*M+(1M:0)); [PEF,n] = covm(F(K+1:N,:),F(K+1:N,:),'M');  PEF = PEF./n; + PEF = PEF./N; [PEB,n] = covm(B(1:NK,:),B(1:NK,:),'M');  PEB = PEB./n; + PEB = PEB./N; %PE{K+1} = PEF; PE(:,K*M+(1:M)) = PEF; end; + elseif Mode==7 %%%%% multichannel Levinsion algorithm [2] using VieiraMorf Method  fprintf('Warning MDURLEV: It''s not recommended to use this mode\n') +elseif Mode==7 %%%%% Partial Correlation Estimation: NutallStrand Method [2] with unbiased covariance estimation C(:,1:M) = C(:,1:M)/N; F = Y; B = Y; @@ 337,8 +307,8 @@ [D,n] = covm(F(K+1:N,:),B(1:NK,:),'M'); D = D./n;  ARF(:,K*M+(1M:0)) = (PEF.^.5)*D*(PEB.^.5);  ARB(:,K*M+(1M:0)) = (PEF.^.5)*D'*(PEB.^.5); + ARF(:,K*M+(1M:0)) = 2*D / (PEB+PEF); + ARB(:,K*M+(1M:0)) = 2*D'/ (PEF+PEB); tmp = F(K+1:N,:)  B(1:NK,:)*ARF(:,K*M+(1M:0)).'; B(1:NK,:) = B(1:NK,:)  F(K+1:N,:)*ARB(:,K*M+(1M:0)).'; @@ 362,9 +332,10 @@ %PE{K+1} = PEF; PE(:,K*M+(1:M)) = PEF; end; + elseif Mode==4, %%%%% Kay, not fixed yet.  fprintf('Warning MDURLEV: It''s not recommended to use this mode\n') + fprintf('Warning MVAR: Mode=4 is broken.\n') C(:,1:M) = C(:,1:M)/N; K = 1; @@ 385,15 +356,16 @@ D = C(:,K*M+(1:M)); for L = 1:K1,  D = D  ARF(:,L*M+(1M:0))*C(:,(KL)*M+(1:M)); + D = D  C(:,(KL)*M+(1:M))*ARF(:,L*M+(1M:0)); end; + ARF(:,K*M+(1M:0)) = PEB \ D; ARB(:,K*M+(1M:0)) = PEF \ D'; for L = 1:K1,  ARFtmp(:,L*M+(1M:0)) = ARF(:,L*M+(1M:0))  ARB(:,(KL)*M+(1M:0)) *ARF(:,K*M+(1M:0)) ;  ARB(:,L*M+(1M:0)) = ARB(:,L*M+(1M:0))  ARF(:,(KL)*M+(1M:0)) *ARB(:,K*M+(1M:0)) ; + tmp = ARF(:,L*M+(1M:0))  ARF(:,K*M+(1M:0))*ARB(:,(KL)*M+(1M:0)); + ARB(:,(KL)*M+(1M:0)) = ARB(:,(KL)*M+(1M:0))  ARB(:,K*M+(1M:0))*ARF(:,L*M+(1M:0)); + ARF(:,L*M+(1M:0)) = tmp; end;  ARF(:,1:(K1)*M) = ARFtmp; RCF(:,K*M+(1M:0)) = ARF(:,K*M+(1M:0)) ; RCB(:,K*M+(1M:0)) = ARB(:,K*M+(1M:0)) ; 