I am trying to understand why the lpc function in the TSA package produces
results different form the function available in Matlab [1]. Here is the
test that I did: first, let us build a signal generated from a AR filter
with known coefficients:
octave> a = poly ([0.95*exp(i*pi/8), 0.95*exp(-i*pi/8)])
a =
1.00000 -1.75537 0.90250
octave> x = [1; zeros(100,1)];
octave> Y = filter (1, a, x);
octave> P = 2;
Now, let us try the three possibilities at the end of the lpc.m file of TSA
(the first one is uncommented):
octave> [AR,RC,PE] = lattice(Y.',P); % Burg method
octave> ar2poly(AR)
ans =
1.00000 -1.34594 0.45876
octave> [AR,RC,PE] = lattice(Y.',P,'GEOL'); % geomatric lattice
octave> ar2poly(AR)
ans =
1.00000 -1.76934 0.91765
octave> [AR,RC,PE] = durlev(acovf(Y.',P)); % Yule-Walker
octave> ar2poly(AR)
ans =
1.00000 -1.75534 0.90247
Clearly, the Burg method produces wrong results. Here is the output of the
Matlab function:
octave> lpc (Y, P)
ans =
1.00000 -1.75534 0.90247
Which is identical (to the displayed precision) to the Yule-Walker method in
TSA's lpc.m.
Could you please fix this in Octave-Forge? The trivial patch is attached
below.
Thanks,
Rafael
[1] http://www.mathworks.com/support/solutions/files/s36350/lpc.m
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