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acovfun.m
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acovfun.m
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function [out, sigma] = acovfun(a, L)
% It builds the autocovariance function of length L and its corresponding
% covariance matrix of an autoregressive process defined by the vector
% parameter a.
%
% It assumes the variance of the input noise to be 1.
%
% It is worth noting that the maximum lag considered is L-1.
%
% INPUT:
% a: coefficients of the autoregressive process.
% L: length of the autocovariance function and dimension of the covariance
% matrix.
%
% OUTPUT:
% out: array with the autocovariance function of length L.
% sigma: LxL covariance matrix.
%
% EXAMPLE:
% rho = 0.90;
% a = [1, -2*rho*cos(pi/3), rho^2];
% L = 50;
% [out, sigma] = acovfun(a, L);
% plot(0:L-1, out);
% xlabel('Lag')
% ylabel('Amplitude')
% title('Autocovariance function')
%
% DEPENDENCIES:
% covAR.m
%
% VERSION:
% 1.0.0 First release.
%
% LAST UPDATE:
% 02/09/2019
if(~exist('covAR.m', 'file'))
error('acovfun requires the function covAR.m');
end
rho = covAR(a, 1);
rho = rho(:)';
% Compute autocovariance function up to lag L-1.
N = length(rho);
out = zeros(1, L);
out(1:min([N, L])) = rho(1:min([N, L]));
for nn = N + 1:L
out(nn) = -sum(fliplr(a(2:end)).*out(nn-N+1:nn-1));
end
sigma = zeros(L, L);
% Build covariance matrix.
for rr = 1:L
for cc = rr:L
sigma(rr, cc) = out(abs(rr - cc) + 1);
sigma(cc, rr) = sigma(rr, cc);
end
end
end