# [FieldTrip] Simulate data to compare methods

tjordanov at besa.de tjordanov at besa.de
Fri Jan 30 17:37:18 CET 2015

```Hi Eelke, hi Jörn,

thank you for your elaborate answers and for the script - it is very informative and useful.
I am in some extent familiar with the theory behind multitapering and I am also convinced that it has very good theoretical properties. However, let us take a look at the application. I simulated 200 trials data with jitter in the frequency. You can find the frequency profile of the trials as attachment ("FrequenciesForSimulation.png"). There are 67 trials with central frequency 34 Hz (variation between 32 and 36 Hz), 67 trials with central frequency 50 Hz (48 to 52 Hz) and 66 trials with central frequency 66 Hz (64 to 68 Hz). I performed multitaper analysis with 1, 2 and 3 tapers (see results "Multitaper1taper.png", "Multitaper2tapers.png", "Multitaper3tapers.png"). As we can see from the results only the decomposition with one taper detected correctly the three frequencies, all other  two methods (with 2 and 3 tapers) just distorted (smoothed) the first result. I can see that such kind of smoothing is good for the statistical power between subjects but it does not prove the advantage of using multiple tapers compared to using just single taper. What do you think?

Best,
Todor

-----Original Message-----
From: fieldtrip-bounces at science.ru.nl [mailto:fieldtrip-bounces at science.ru.nl] On Behalf Of Jörn M. Horschig
Sent: Freitag, 30. Januar 2015 13:34
To: 'FieldTrip discussion list'
Subject: Re: [FieldTrip] Simulate data to compare methods

Hi Todor,

maybe this matlab function helps illustrating what dpss multitapers are, and will thus clarify what makes them so powerful compared to other techniques:
https://www.dropbox.com/s/0uifk9l8rb6m5vl/Tapering.m?dl=0
(go to example 5)

Best,
Jörn

--

Jörn M. Horschig, Software Engineer
Artinis Medical Systems  |  +31 481 350 980

> -----Original Message-----
> From: fieldtrip-bounces at science.ru.nl [mailto:fieldtrip-
> bounces at science.ru.nl] On Behalf Of Eelke Spaak
> Sent: Friday, January 30, 2015 11:52 AM
> To: FieldTrip discussion list
> Subject: Re: [FieldTrip] Simulate data to compare methods
>
> Hi Todor,
>
> Although your procedure would also yield smoothing in the frequency
> domain which is independent from that in the time domain, it is not at
> all equivalent to using multitapers!
>
> The tapers in the discrete prolate spheroidal sequence (dpss, ==
> multitaper in fieldtrip) are pairwise orthogonal, hence their
> estimates are independent from one another. This will result in there
> being more information extracted from the signal than if you used a
> single taper and then apply Gaussian smoothing over frequencies. You
> could have a look at https://en.wikipedia.org/wiki/Multitaper which
> gives quite a decent overview of multitapering. Or for the full
> details, refer to the original paper by David Thompson:
> http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1456701
>
> Best.
> Eelke
>
> On 30 January 2015 at 11:10, tjordanov at besa.de <tjordanov at besa.de>
> wrote:
> > Hi Eelke,
> >
> > I found your answer very interesting. If I understand you correctly,
> > the
> advantage of the multitaper method is that it smoothes in the
> frequency domain independently of the smoothing in the time domain.
> Then it should be equivalent (or similar) with the following procedure:
> > 1) Calculate single trial single taper decomposition of the signal.
> > 2) Choose an appropriate 1D Gauss function (note that it is
> > important to be 1D else it would smooth in both - time and
> > frequency)
> > 3) Apply the selected Gauss function on the decomposed signal only
> > in the
> frequency direction (not in time in order to avoid temporal smearing).
> Do this for all trials and all time points.
> > 4) Calculate the average over the trials.
> > In this procedure the choice of the Gaussian would determine the
> > amount
> of smearing in the frequency domain.
> >
> > Is this so, or I misunderstood something?
> >
> > Best,
> > Todor
> >
> >
> > -----Original Message-----
> > From: fieldtrip-bounces at science.ru.nl
> > [mailto:fieldtrip-bounces at science.ru.nl] On Behalf Of Eelke Spaak
> > Sent: Mittwoch, 28. Januar 2015 12:24
> > To: FieldTrip discussion list
> > Subject: Re: [FieldTrip] Simulate data to compare methods
> >
> > Hi Nico,
> >
> > As for question (2), you probably first need to think about what
> > constitutes
> a "better" result. Using more tapers with dpss will always result in
> more frequency smoothing. If your source signal is primarily composed
> of pure sinusoids, and you interpret a spectrum as "better"
> > if it shows clearer peaks, then you will always get the "best"
> > result for the
> single-taper case.
> >
> > Multitapering allows optimal control over the amount of smoothing
> > you
> obtain in the frequency domain, which is more or less independent of
> the amount of smoothing you obtain in the time domain (as opposed to e.g.
> wavelets, where these are fundamentally linked). When dealing with
> brain signals, you will often find that a certain stimulus might
> induce e.g. a gamma response at 40-50 Hz in one subject and one trial,
> while in another subject or another trial the same stimulus might
> induce a 50-60 Hz response or so. Of course, in the average over
> trials (and subjects), this heterogeneity (i.e.,
> noise) will wash out, but it will severely damage your statistical sensitivity.
> Therefore, using multitapers to add smoothing can produce a much more
> consistent result and therefore be "better" in the sense of actually
> understanding the brain.
> >
> > As for your simulation, perhaps using filtered noise would be better
> > than
> sinusoids. Also, since multitapering benefits you most strongly when
> taking variation over observations into account, you could consider
> simulating different observations, each consisting of noise filtered
> in a slightly different randomly chosen bandwidth, and inspecting the
> resulting variation over observations in the spectra.
> >
> > Best,
> > Eelke
> >
> > On 27 January 2015 at 18:36, Max Cantor <mcantor at umich.edu> wrote:
> >> Hi Nico,
> >>
> >> I'm not sure about the second question, but as for the first
> >> question, you can manually set the scales for ft_singleplotTFR
> >> using
> cfg.zlim.
> >>
> >> Hope that helps,
> >>
> >> Max
> >>
> >> On Tue, Jan 27, 2015 at 11:50 AM, Nico Weeger
> >> wrote:
> >>>
> >>> Hello FieldTrip community,
> >>>
> >>>
> >>>
> >>> I am new to FieldTrip and I try to simulate data to compare the
> >>> ft_frequanalysis methods Hanning, Multitaper and Wavelet.
> >>>
> >>> Therefore I simulate Data manually using different latency,
> >>> amplitude and frequency combinations using the following equation:
> >>>
> >>> sig1 = exp(-(t-lat1).^2/(2*sigma1))*amp1.*sin(2*pi*f1*t);
> >>>
> >>> sig2 = exp(-(t-lat2).^2/(2*sigma2))*amp2.*sin(2*pi*f2*t);
> >>>
> >>> sig3 = exp(-(t-lat1).^2/(2*sigma1))*amp1.*sin(2*pi*f2*t);
> >>>
> >>> sig4 = exp(-(t-lat2).^2/(2*sigma2))*amp2.*sin(2*pi*f1*t);
> >>>
> >>> sig = sig1+sig2+sig3+sig4;
> >>>
> >>> where amp1=20; amp2 = 5; lat1= 1.7; lat2 = 2.3; f1 = 12; f2 = 60;
> >>>
> >>>
> >>> After using ft_frequanalysis (see the following cfgs)
> >>>
> >>>
> >>> Cfg Wavelet:
> >>>
> >>> cfg = [];
> >>>
> >>> cfg.output     = 'pow';
> >>>
> >>> cfg.channel    = labels;
> >>>
> >>> cfg.method     = 'wavelet';
> >>>
> >>> cfg.width      = 7;
> >>>
> >>> cfg.gwidth     = 3;
> >>>
> >>> cfg.foilim     = [1 70];
> >>>
> >>> cfg.toi        = 0:0.05:2;
> >>>
> >>> TFRwave = ft_freqanalysis(cfg, data_preproc);
> >>>
> >>>
> >>>
> >>> Cfg Hanning / Multitaper:
> >>>
> >>> cfg = [];
> >>>
> >>> cfg.output     = 'pow';
> >>>
> >>> cfg.channel    = labels;
> >>>
> >>> cfg.method     = 'mtmconvol'
> >>>
> >>> cfg.foi        = 1:1:70
> >>>
> >>> cfg.tapsmofrq  = 0.2*cfg.foi;
> >>>
> >>> cfg.taper      = 'dpss' / ‘hanning’;
> >>>
> >>> cfg.t_ftimwin  = 4./cfg.foi;
> >>>
> >>> cfg.toi        = 0:0.05:2;
> >>>
> >>> TFRmult1 = ft_freqanalysis(cfg, data_preproc);
> >>>
> >>>
> >>>
> >>>
> >>> the data is plotted with ft_singleplotTFR (see cfg below)
> >>>
> >>>
> >>> cfg singleplot:
> >>>
> >>> cfg = [];
> >>>
> >>>
> >>> cfg.colorbar     = 'yes';
> >>>
> >>> cfg.layout       = 'AC_Osc.lay';
> >>>
> >>> ft_singleplotTFR(cfg, TFRwave);
> >>>
> >>>
> >>> Two problems occur. First, the power scale of wavelet and
> >>> Multitaper/Hanning differs extremely (Multi 0-~100 and Wavelet 0-
> ~15*10^4).
> >>>
> >>> 1.       How can I get the scale of all methods equal, or do I have to
> >>> change the Wavelet settings to get the right scale of the values?
> >>>
> >>> Second, the best result of Multitaper analysis is performed using
> >>> only one Taper. The goal was to get a result, where the advantages
> >>> and disadvantages of Multitaper analysis compared to the other
> methods can be seen.
> >>>
> >>> 2.       How can I change the simulation so that more tapers show better
> >>> results than a single taper does?
> >>>
> >>>
> >>> Thank you for your time and help.
> >>>
> >>>
> >>> Regards,
> >>>
> >>>
> >>>
> >>> Nicolas Weeger
> >>>
> >>> Student of Master-Program Appied Research,
> >>>
> >>> University Ansbach,
> >>>
> >>> Germany
> >>>
> >>>
> >>> _______________________________________________
> >>> fieldtrip mailing list
> >>> fieldtrip at donders.ru.nl
> >>> http://mailman.science.ru.nl/mailman/listinfo/fieldtrip
> >>
> >>
> >>
> >>
> >> --
> >> Max Cantor
> >> Lab Manager
> >> Computational Neurolinguistics Lab
> >> University of Michigan
> >
> > _______________________________________________
> > fieldtrip mailing list
> > fieldtrip at donders.ru.nl
> > http://mailman.science.ru.nl/mailman/listinfo/fieldtrip
> >
> >
> > _______________________________________________
> > fieldtrip mailing list
> > fieldtrip at donders.ru.nl
> > http://mailman.science.ru.nl/mailman/listinfo/fieldtrip
>
> _______________________________________________
> fieldtrip mailing list
> fieldtrip at donders.ru.nl
> http://mailman.science.ru.nl/mailman/listinfo/fieldtrip

_______________________________________________
fieldtrip mailing list
fieldtrip at donders.ru.nl
http://mailman.science.ru.nl/mailman/listinfo/fieldtrip
-------------- next part --------------
A non-text attachment was scrubbed...
Name: FrequenciesForSimulation.png
Type: image/png
Size: 6793 bytes
Desc: not available
URL: <http://mailman.science.ru.nl/pipermail/fieldtrip/attachments/20150130/3098a6ef/attachment-0008.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Multitaper1taper.png
Type: image/png
Size: 6344 bytes
Desc: not available
URL: <http://mailman.science.ru.nl/pipermail/fieldtrip/attachments/20150130/3098a6ef/attachment-0009.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Multitaper2tapers.png
Type: image/png
Size: 6301 bytes
Desc: not available
URL: <http://mailman.science.ru.nl/pipermail/fieldtrip/attachments/20150130/3098a6ef/attachment-0010.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Multitaper3tapers.png
Type: image/png
Size: 6207 bytes
Desc: not available
URL: <http://mailman.science.ru.nl/pipermail/fieldtrip/attachments/20150130/3098a6ef/attachment-0011.png>
```