Why is filtic/arburg not working how I intend it to?

Question

Joseph Ravenscroft 2017-1-29

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/322348-why-is-filtic-arburg-not-working-how-i-intend-it-to

回答： Greg Dionne 2017-1-30

So I'm trying to construct a simple autoregressive algorithm that can predict the output samples for a sine wave using the Burg method. My issue is that I have a discontinuity at the start and end, and perhaps I am incorrect, but I believe it is to do with the initial conditions being set incorrectly to the filter.

The reconstructed output looks like this:

As you can see from the bottom figure the filter is starting with an initial sample value of 0.5 rather than what should be around 0.9.

Here is my code:

    % Begin Burg Method process
  coef_number = 3;
  burg_start_coef = arburg(x_start, coef_number);
  burg_end_coef = arburg(x_end, coef_number);
start_cond = filtic(1, burg_start_coef, x_start);
end_cond = filtic(1, burg_end_coef, x_end);
start_result = filter(1, burg_start_coef, zeros(1, counter), start_cond);
end_result = filter(1, burg_end_coef, zeros(1, counter), end_cond);
xfade = zeros(1, counter);
for i = 1:counter
   xfade(i) = 0.5*cos(i*pi/counter) + 0.5; 
end
start_result = start_result.*xfade;
end_result = end_result.*xfade;
% Flip the end array so it is no longer reversed
end_result = fliplr(end_result);
result = start_result + end_result;
x_predicted(1:3000) = x_corrupted(1:3000);
x_predicted(3001:4000) = result;
x_predicted(4001:N) = x_corrupted(4001:N);
% Plot initial extrapolations
subplot(5, 1, 1)
plot(start_result)
subplot(5, 1, 2)
plot(end_result)
subplot(5, 1, 3)
plot(xfade)
subplot(5, 1, 4)
plot(result)
subplot(5, 1, 5)
plot(x_predicted)