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function [ACF,NN] = acovf(Z,KMAX,Mode,Mode2);
% ACOVF estimates autocovariance function (not normalized)
% NaN's are interpreted as missing values.
%
% [ACF,NN] = acovf(Z,MAXLAG,Mode);
%
% Input:
% Z Signal (one channel per row);
% MAXLAG maximum lag
% Mode 'biased' : normalizes with N [default]
% 'unbiased': normalizes with N-lag
% 'coeff' : normalizes such that lag 0 is 1
% others : no normalization
%
% Output:
% ACF autocovariance function
% NN number of valid elements
%
% REFERENCES:
% A.V. Oppenheim and R.W. Schafer, Digital Signal Processing, Prentice-Hall, 1975.
% S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
% M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
% W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
% J.S. Bendat and A.G.Persol "Random Data: Analysis and Measurement procedures", Wiley, 1986.
% $Id$
% Copyright (C) 1998-2003,2008,2010 by Alois Schloegl <alois.schloegl@gmail.com>
% This is part of the TSA-toolbox. See also
% http://biosig-consulting.com/matlab/tsa/
%
% 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/>.
if nargin<3, Mode='biased'; end;
[lr,lc] = size(Z);
MISSES = sum(isnan(Z)')';
if any(MISSES); % missing values
M = real(~isnan(Z));
Z(isnan(Z))=0;
end;
if (nargin == 1)
KMAX = lc-1;
elseif (KMAX >= lc-1)
KMAX = lc-1;
end;
ACF = zeros(lr,KMAX+1);
if nargin>3, % for testing, use arg4 for comparing the methods,
elseif (KMAX*KMAX > lc*log2(lc)) % & isempty(MISSES);
Mode2 = 1;
elseif (10*KMAX > lc);
Mode2 = 3;
else
Mode2 = 4;
end;
%%%%% ESTIMATION of non-normalized ACF %%%%%
% the following algorithms gve equivalent results, however, the computational effort is different,
% depending on lr,lc and KMAX, a different algorithm is most efficient.
if Mode2==1; % KMAX*KMAX > lc*log(lc); % O(n.logn)+O(K)
tmp = fft(Z',2^nextpow2(size(Z,2))*2);
tmp = ifft(tmp.*conj(tmp));
ACF = tmp(1:KMAX+1,:)';
if ~any(any(imag(Z))), ACF=real(ACF); end; % should not be neccessary, unfortunately it is.
elseif Mode2==3; % (10*KMAX > lc) % O(n*K) % use fast Built-in filter function
for L = 1:lr,
acf = filter(Z(L,lc:-1:1),1,Z(L,:));
ACF(L,:)= acf(lc:-1:lc-KMAX);
end;
else Mode2==4; % O(n*K)
for L = 1:lr,
for K = 0:KMAX,
ACF(L,K+1) = Z(L,1:lc-K) * Z(L,1+K:lc)';
end;
end;
end;
%%%%% GET number of elements used for estimating ACF - is needed for normalizing ACF %%%%%
if any(MISSES),
% the following algorithms gve equivalent results, however, the computational effort is different,
% depending on lr,lc and KMAX, a different algorithm is most efficient.
if Mode2==1; % KMAX*KMAX > lc*log(lc); % O(n.logn)+O(K)
tmp = fft(M',2^nextpow2(size(M,2))*2);
tmp = ifft(tmp.*conj(tmp));
NN = tmp(1:KMAX+1,:)';
if ~any(any(imag(M))), NN=real(NN); end; % should not be neccessary, unfortunately it is.
elseif Mode2==3; % (10*KMAX > lc) % O(n*K) % use fast Built-in filter function
for L = 1:lr,
acf = filter(M(L,lc:-1:1),1,M(L,:));
NN(L,:)= acf(lc:-1:lc-KMAX);
end;
else Mode2==4; % O(n*K)
for L = 1:lr,
for K = 0:KMAX,
NN(L,K+1) = M(L,1:lc-K) * M(L,1+K:lc)';
end;
end;
end;
else
NN = (ones(lr,1)*(lc:-1:lc-KMAX));
end;
if strcmp(Mode,'biased')
if ~any(MISSES),
ACF=ACF/lc;
else
%ACF=ACF./((lc-MISSES)*ones(1,KMAX+1));
ACF=ACF./max(NN + ones(lr,1)*(0:KMAX),0);
end;
elseif strcmp(Mode,'unbiased')
ACF=ACF./NN;
%if ~any(MISSES),
% ACF=ACF./(ones(lr,1)*(lc:-1:lc-KMAX));
%else
% ACF=ACF./((lc-MISSES)*ones(1,KMAX+1) - ones(lr,1)*(0:KMAX));
%end;
elseif strcmp(Mode,'coeff')
%ACF = ACF ./ ACF(:,ones(1,KMAX+1)) .* ((lc-MISSES)*ones(1,KMAX+1));
ACF = ACF./NN;
ACF = ACF./(ACF(:,1)*ones(1,size(ACF,2)));
else
end;
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