[FieldTrip] Simulate data to compare methods
Jörn M. Horschig
jorn at artinis.com
Fri Jan 30 13:34:16 CET 2015
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
> >> <nico.weeger at googlemail.com>
> >> 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.maskstyle = 'saturation';
> >>>
> >>> 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
> >
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> >
> >
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