[FieldTrip] Questions about the phase estimation using multiple-tapper analysis.

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

Dear Ruoyi,

Yes! It makes sense to use the multitaper method in order to compute your spectral quantities. It is exactly the multitaper property - that it does ’spectral concentration’, or ‘controlled leakage’, or ‘variance reduction on the spectral estimates’ (all just different wordings for the same thing) - which boosts your sensitivity to detect band-limited effects, both in power or phase-difference-consistency metrics. Long story short: if the bandwidth of your spectral component is larger than the nominal spectral resolution that’s provided by your single taper spectral decomposition method, then there will be a benefit of multitapering.

Below is some simulation code that demonstrates this (on purpose I titrated the parameters of the simulation to show the effect). The bottom line is, that I simulate a band-limited effect of connectivity (and power) in the ‘beta’ band, between 15 and 25 Hz. If I do a spectral decomposition using a single Hanning taper on one-second long epochs, my nominal frequency resolution will be 1 Hz per frequency bin, which means that I don’t optimally capture the whole signal (bandwidth = 10 Hz) with the individual frequency bins. When I use multitapers, the ‘point estimates’ of the individual frequency bins are now somewhat less precise in frequency (because of the spectral smoothing of - in this case - +/- 4 Hz), but this is compensated for by more robust phase difference estimates, and thus by peaks in the plv spectrum that are more convincing to the eye (and eventually also more convincing to the inferential statistical machinery).

If you are convinced by this little simulation, could I ask you to consider to make this a FAQ or example script on the fieldtrip website? This will yield a more persistent record of our efforts to enlighten one another than the volatile e-mail discussion list.

Best wishes and keep up the good work,
Jan-Mathijs



% create some dummy data
fsample = 1000;
N       = 100000; % number of samples for 100 s



noise(1,:) = cumsum(randn(1,N));
noise(2,:) = cumsum(randn(1,N));
noise   = noise - mean(noise,2);



dat     = ft_preproc_bandpassfilter(randn(2,N), 1000, [15 25], [], 'firws');





data = [];
data.label = {'chan01';'chan02'};
data.trial = {noise/8 + [0.7 0.3;0.3 0.7]*dat};
data.time  = {(0:(N-1))./fsample};



% chop in 1 second epochs
cfg = [];
cfg.length = 1;
data = ft_redefinetrial(cfg, data);



% spectral analysis
cfg = [];
cfg.method = 'mtmfft';
cfg.output = 'fourier';
cfg.taper  = 'hanning';
cfg.foilim = [0 60];
freqH = ft_freqanalysis(cfg, data);
cfg.taper  = 'dpss';
cfg.tapsmofrq = 4;
freqM = ft_freqanalysis(cfg, data);



% connectivity analysis
cfg = [];
cfg.method = 'plv';
plvH = ft_connectivityanalysis(cfg, freqH);
plvM = ft_connectivityanalysis(cfg, freqM);



% visualization
cfg = [];
cfg.parameter = 'plvspctrm';
ft_connectivityplot(cfg, plvH, plvM);



On 5 Apr 2021, at 17:23, Ruoyi Cao <ruoyi.cao at mail.huji.ac.il<mailto:ruoyi.cao at mail.huji.ac.il>> wrote:

Dear Community:
My name is Ruoyi.Cao and I am a PhD student in Leon Deouell lab in Hebrew University of Jerusalem. I am currently working on Functional connectivity data during working memory delay. In the experiment, I compared 2 PLV value between two conditions.
The analysis followed the tutorial
https://www.fieldtriptoolbox.org/tutorial/connectivity/
For the functional connectivity, Instead of coherence, I computed the PLV value.

Here is the step :
1: I first get fourier coefficient of the data by
cfg           = [];
cfg.method    =  'mtmfft';
cfg.taper     = 'dpss';%
cfg.output    = 'fourier';
cfg.tapsmofrq =3
cfg.foi          = 1:2:60
Tapper3freqB2{1}  = ft_freqanalysis(cfg, DataB2);

2:Then I put this output
cfg           = [];
cfg.method    = 'plv';
plvfreqB2 {P}          = ft_connectivityanalysis(cfg, Tapper3freqB2{1} );

Finally, I compared the plv value between conditions and found a robust cluster through cluster-based permutation test.  However, I cannot replicate the significant contrast between conditions if I used hanning window with standard fft for calculating fourier coefficient.

I am writing to ask whether it makes sense to use all the output of multi-tapper method, which is 3 times (taper number is 3) the original trial number to compute the PLV value. What is the influence of the phase estimation that muti-tapper analysis could cause. If the above procedure is not wrong,  why the same results can not be replicated with hanning window using one tapper.

Thank you so much
Best
Ruoyi




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