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Linear predictive extrapolation
% This code answers the question at http://dsp.stackexchange.com/a/110/64
N = 150; % Order of LPC auto-regressive model
P = 500; % Number of samples in the extrapolated time series
M = 150; % Point at which to start predicting
t = 1:P;
x = 5*sin(t/3.7+.3)+3*sin(t/1.3+.1)+2*sin(t/34.7+.7); %This is the measured signal
a = arburg(x, N);
y = zeros(1, P);
% fill in the known part of the time series
y(1:M) = x(1:M);
% Run the initial timeseries through the filter to get the filter state
[~, zf] = filter(-[0 a(2:end)], 1, x(1:M));
% Now use the filter as an IIR to extrapolate
y((M+1):P) = filter([0 0], -a, zeros(1, P-M), zf);
% The above filter command can be replaced with this for-loop:
%
% for ii=(M+1):P
% y(ii) = -sum(a(2:end) .* y((ii-1):-1:(ii-N)));
% end
plot(t, x, ... % signal
t, y, ... % extrapolation
t, x - y); % difference
l = line(M*[1 1], get(gca, 'ylim'));
set(l, 'color', [0,0,0]);
legend('actual signal', 'extrapolated signal', 'error','start of extrapolation');
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