[Eeglablist] changes in spectopo?

[Thomas Ferree]

Dear all,
As I understand it, the multi-taper is an extension of Welch.  In
Welch, the data are tapered with a raised and scaled cosine
(ranging 0-1) or something similar, in order to force periodicity.
Otherwise the discontinuity that arises when the data are
periodically continued gives rise to massive spectral leakage.
The disadvantage of Welch is that the cosine function keeps the
middle of the data segment entirely but loses the ends entirely,
so roughly half the data is lost.  Multi-taper uses a set of tapers,
not just a cosine, and thereby keeps more data.  Actually the
derivation of multi-taper involves finding the statistical estimate
of the power spectrum with least variance, same as the way
Welch determined to use 50% overlap with cosine tapers,
but the effect is that multi-taper keeps more of the data. It is
true that one must pick the number of tapers, and computing
the spectrum takes more time.  From this reasoning, multi-taper
is preferable always on theoretical grounds, and when you can't
afford to lose data on practical grounds.
Hope this helps, Tom.


On Sun, Aug 9, 2009 at 11:37 PM, Arnaud Delorme <arno at ucsd.edu> wrote:

> Dear Wambua,
>
> you should most likely use the pwelch method (implemented in the
> EEGLAB spectopo function). It is a windowed FFT (several FFT averaged).
> The Thomson method (usually known as multitaper) is good too. It is
> first projecting the data onto an orthogonal base, then performing FFT.
>
> They should all return similar results (FFT, pwelch, multitaper). I
> guess the Thomson method is the less sensitive to noise but also the
> most complex to use. I guess it would also be possible to use the
> welch method on top of multitaper. It is all a matter of preference. I
> would advised using the pwelch method which is easy (you just give as
> an option the length of the windows and the overlap). Multitaper would
> require you to select the number of basis vector in your othogonal
> base and this is much less intuitive (and also has consequences on the
> frequency resolution you can achive).
>
> Hope this helps,
>
> Arno
>
>
> On Aug 6, 2009, at 12:22 PM, Wambua Kazi wrote:
>
> > Dear esteemed colleagues,
> >     I am trying the estimate the mean EEG spectra of epoched data.
> > I addition to an FFT, there are at least two methods implemented in
> > Matlab for this purpose: [1] pwelch.m (Welch's method, EEGLAB uses
> > this) and [2] pmtm.m (Thomson's multitaper method).
> >     Can anyone tell me what the relative pro's and con's of the
> > Welch and Thomson method are for about 1-2 second epoched data
> > (around 256-512 time points)?
> >             thank you for your time,
> >                      -Wambua
> >
> >
> > <ATT00001.txt>
>
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-- 
Thomas Ferree, PhD
Department of Radiology
UT Southwestern Medical Center
Email: tom.ferree at gmail.com
Voice: (214) 648-9767
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