[FieldTrip] Spectral factorization: Wilson-Burg algorithm does not converge

[Schoffelen, J.M. (Jan Mathijs)]

Hi Mitch,

It could be that your dysconvergence is due to 1) you using a wavelet transform, and 2) you using a very limited bandwidth. In my experience the algorithm performs best if you use a multitapered FFT approach, estimating frequencies from 0 up until the Nyquist frequency, and using a lot of zero-padding before the spectral estimation.

Best,
Jan-Mathijs
 

On Nov 29, 2015, at 7:43 PM, vpapenm at uni-koeln.de wrote:

> 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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