[FieldTrip] Spectral factorization: Wilson-Burg algorithm does not converge
vpapenm at uni-koeln.de
vpapenm at uni-koeln.de
Sun Nov 29 19:43:02 CET 2015
Dear all,
I use sfactorization_wilson.m (in my own pipeline outside field trip
actually) to estimate the spectral Granger causality of my time series
(local field potentials from deep brain stimulation electrodes). As
input I use a 3D spectral matrix S with dimensions 2x2x32 calculated
from wavelet transformation at frequencies f=[0:1:31] Hz. It consists
of time-averaged auto- (Sxx, Syy) and cross-spectral densities (Sxy,
conj(Sxy)), obtained from smoothing the wavelet matrix.
My problem is that the implemented Wilson-Burg algorithm quite often
does not converge at all and I wonder if anybody else has that
problem. The non-convergence leads to a new spectral matrix
Snew=psi*psi', which has non-zero imaginary parts or which is simply
too different from the original matrix S.
I also wonder why the only criteria to stop the iteration is when the
increment step psi_old-psi becomes small. Why is there no criterion to
stop the iteration if the new spectral matrix is close enough to the
original one (e.g. S-Snew<tol)?
At the moment I have tried two different approaches to estimate the
power at f=0 Hz: 1) I use the power at f=0Hz from FFT [which is mean(
sum(x).^2/N*dt ); for the auto-spectra, e.g.] and 2) I use a linear
extrapolation of the PSD to get P(f=0). However, both methods do not
lead to sufficient convergence of the algorithm.
I would be very grateful if someone found the time to answer.
Best regards,
Mitch
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