<div><br></div><div>Dear all,</div><div>As I understand it, the multi-taper is an extension of Welch. In</div><div>Welch, the data are tapered with a raised and scaled cosine </div><div>(ranging 0-1) or something similar, in order to force periodicity.</div>
<div>Otherwise the discontinuity that arises when the data are</div><div>periodically continued gives rise to massive spectral leakage.</div><div>The disadvantage of Welch is that the cosine function keeps the</div><div>middle of the data segment entirely but loses the ends entirely,</div>
<div>so roughly half the data is lost. Multi-taper uses a set of tapers,</div><div>not just a cosine, and thereby keeps more data. Actually the</div><div>derivation of multi-taper involves finding the statistical estimate</div>
<div>of the power spectrum with least variance, same as the way </div><div>Welch determined to use 50% overlap with cosine tapers,</div><div>but the effect is that multi-taper keeps more of the data. It is</div><div>true that one must pick the number of tapers, and computing</div>
<div>the spectrum takes more time. From this reasoning, multi-taper </div><div>is preferable always on theoretical grounds, and when you can't </div><div>afford to lose data on practical grounds.</div><div>Hope this helps, Tom.</div>
<br><br><div class="gmail_quote">On Sun, Aug 9, 2009 at 11:37 PM, Arnaud Delorme <span dir="ltr"><<a href="mailto:arno@ucsd.edu">arno@ucsd.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Dear Wambua,<br>
<br>
you should most likely use the pwelch method (implemented in the<br>
EEGLAB spectopo function). It is a windowed FFT (several FFT averaged).<br>
The Thomson method (usually known as multitaper) is good too. It is<br>
first projecting the data onto an orthogonal base, then performing FFT.<br>
<br>
They should all return similar results (FFT, pwelch, multitaper). I<br>
guess the Thomson method is the less sensitive to noise but also the<br>
most complex to use. I guess it would also be possible to use the<br>
welch method on top of multitaper. It is all a matter of preference. I<br>
would advised using the pwelch method which is easy (you just give as<br>
an option the length of the windows and the overlap). Multitaper would<br>
require you to select the number of basis vector in your othogonal<br>
base and this is much less intuitive (and also has consequences on the<br>
frequency resolution you can achive).<br>
<br>
Hope this helps,<br>
<br>
Arno<br>
<br>
<br>
On Aug 6, 2009, at 12:22 PM, Wambua Kazi wrote:<br>
<br>
> Dear esteemed colleagues,<br>
> I am trying the estimate the mean EEG spectra of epoched data.<br>
> I addition to an FFT, there are at least two methods implemented in<br>
> Matlab for this purpose: [1] pwelch.m (Welch's method, EEGLAB uses<br>
> this) and [2] pmtm.m (Thomson's multitaper method).<br>
> Can anyone tell me what the relative pro's and con's of the<br>
> Welch and Thomson method are for about 1-2 second epoched data<br>
> (around 256-512 time points)?<br>
> thank you for your time,<br>
> -Wambua<br>
><br>
><br>
> <ATT00001.txt><br>
<br>
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</blockquote></div><br><br clear="all"><br>-- <br>Thomas Ferree, PhD<br>Department of Radiology<br>UT Southwestern Medical Center<br>Email: <a href="mailto:tom.ferree@gmail.com">tom.ferree@gmail.com</a><br>Voice: (214) 648-9767<br>