--- /dev/null
+function [w,A,B,R,P,F,ip] = ar_spa(ARP,nhz,E);
+% AR_SPA decomposes an AR-spectrum into its compontents
+% [w,A,B,R,P,F,ip] = ar_spa(AR,fs,E);
+%
+% INPUT:
+% AR autoregressive parameters
+% fs sampling rate, provide w and B in [Hz], if not given the result is in radians
+% E noise level (mean square), gives A and F in units of E, if not given as relative amplitude
+%
+% OUTPUT
+% w center frequency
+% A Amplitude
+% B bandwidth
+% - less important output parameters -
+% R residual
+% P poles
+% ip number of complex conjugate poles
+% real(F) power, absolute values are obtained by multiplying with noise variance E(p+1)
+% imag(F) assymetry, - " -
+%
+% All input and output parameters are organized in rows, one row
+% corresponds to the parameters of one channel
+%
+% see also ACOVF ACORF DURLEV IDURLEV PARCOR YUWA
+%
+% REFERENCES:
+% [1] Zetterberg L.H. (1969) Estimation of parameter for linear difference equation with application to EEG analysis. Math. Biosci., 5, 227-275.
+% [2] Isaksson A. and Wennberg, A. (1975) Visual evaluation and computer analysis of the EEG - A comparison. Electroenceph. clin. Neurophysiol., 38: 79-86.
+% [3] G. Florian and G. Pfurtscheller (1994) Autoregressive model based spectral analysis with application to EEG. IIG - Report Series, University of Technolgy Graz, Austria.
+
+% $Id: ar_spa.m 5090 2008-06-05 08:12:04Z schloegl $
+% Copyright (C) 1996-2003 by Alois Schloegl <a.schloegl@ieee.org>
+% This is part of the TSA-toolbox see also:
+% http://hci.tugraz.at/schloegl/matlab/tsa/
+% http://octave.sf.net/
+%
+% 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 3 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, see <http://www.gnu.org/licenses/>.
+
+
+[NTR,pp]=size(ARP);
+
+R=zeros(size(ARP));
+P=zeros(size(ARP));
+w=zeros(size(ARP));
+A=zeros(size(ARP));
+B=zeros(size(ARP));
+F=zeros(size(ARP));
+F1 = F;
+for k = 1:NTR, %if ~mod(k,100),k, end;
+ [r,p,tmp] = residue(1,[1 -ARP(k,:)]);
+ [tmp,idx] = sort(-abs(r));
+ R(k,:) = r(idx)'; % Residual,
+ P(k,:) = p(idx)'; % Poles
+ %r(k,:)=roots([1 -ARP(k,:)])';
+ w(k,:) = angle(p(idx)'); % center frequency (in [radians])
+ A(k,:) = 1./abs(polyval([1 -ARP(k,:)],exp(i*w(k,:)))); % Amplitude
+ %A(k,:) = freqz(1,[1 -ARP(k,:)],w(k,:)); % Amplitude
+ %A2(k,:) = abs(r)'./abs(exp(i*w(k,:))-r'); % Amplitude
+ B(k,:) = -log(abs(p(idx)')); % Bandwidth
+
+ if nargout < 6,
+
+ elseif 0,
+ F(k,:) = (1+sign(imag(r(idx)')))./(polyval([-ARP(k,pp-1:-1:1).*(1:pp-1) pp],1./p(idx).').*polyval([-ARP(k,pp:-1:1) 1],p(idx).'));
+
+ elseif 1;
+ a3 = polyval([-ARP(k,pp-1:-1:1).*(1:pp-1), pp],1./p(idx).');
+ a = polyval([-ARP(k,pp:-1:1) 1],p(idx).');
+ %F(k,:) = (1+(imag(P(k,:))~=0))./(a.*a3);
+ F(k,:) = (1+sign(imag(P(k,:))))./(a.*a3);
+ end;
+end;
+
+A = A.*sqrt(E(:,ones(1,pp))/(2*pi*nhz));
+if nargin>1,
+ if size(nhz,1)==1,
+ nhz = nhz(ones(NTR,1),:);
+ end;
+ w = w.*nhz(:,ones(1,pp))/(2*pi);
+ B = B.*nhz(:,ones(1,pp))/(2*pi);
+end;
+if nargin>2,
+ F = F.*E(:,ones(1,pp));
+ F1 = F1.*E(:,ones(1,pp));
+end;
+
+ip = sum(imag(P)~=0,2)/2;
+return;
+
+np(:,1) = sum(imag(P')==0)'; % number of real poles
+np(:,2) = pp-np(:,1); % number of imaginary poles
+
+