theta harmonics with wavelets

[Demetris Roumis]

Hi Mike,

This may not be the appropriate place for this, in which case feel free to ignore this or maybe we can take this into an email instead.

I read a recent paper, linked below, which seems to do a pretty nice job comparing the spectral analysis methods of wavelet, ensemble empirical-mode decomposition, and Fourier transform.

(open acces)

https://www.eneuro.org/content/early/2019/07/19/ENEURO.0142-19.2019

They argue that the way previous wavelet analysis has been done has led to the error of misinterpreting theta harmonics as a broad 'slow gamma' (~25-50Hz) in hippocampus. They basically imply that wavelets aren't great, without offering much in the way of best practices.

I did not see much of a discussion about harmonics in ANTSD, so my general question is about whether you have specific recommendations for detecting/avoiding such issues.. i.e. could/should wavelet parameters be chosen specifically to avoid distortion of harmonics?

Related question, I know that increasing the number of wavelets for higher frequencies will somewhat compensate and tighten the frequency resolution, at least giving a more accurate result that could help in the detection of harmonics. In the book you recommend a range 3-14 cycles; is there a principled way of choosing this range? I'm generally interested in 4-300 Hz, which is a higher end than most analysis in your book, so would you recommend more than 14 cycles on the high end or is there some reason why 14 cycles should not be exceeded?

Thanks so much!

Best,

Demetris

[Mike X Cohen]

Hi Demetris. This list is definitely the right place to ask questions about papers like this.

I'm a bit surprised to see it published in this form, to be honest. I gave feedback on an unpublished version of this manuscript, which was not incorporated into the final version. My comments are below and code is attached for you to investigate further (just run the STFFT... script; the other two are supporting files given to me by the authors to reproduce their simulation). 

Regarding your second question, see this paper. And let me know if you have more questions.

1) I don't see the benefit of including EMD. It's a shitty method for neural data, and -- with the exception of a few enthusiastic methodologists -- it's exceedingly rarely used in empirical papers.

2) The claim that Morlet wavelet convolution is suboptimal seems disingenuous to me. It feels like the paper was set out a priori to trash wavelet convolution for some reason (no offense, I promise, that's just what I feel from the tone), and yet it was pretty trivial for me to come to the exact opposite conclusion -- that wavelet convolution is accurate (though smooth) while Welch's method is crap. See attached code (n.b. I took a few coding short-cuts here and there in the interest of time, but that doesn't change the conclusions). You can also change the window size parameter on line 61 to get the results to match more closely.

3) I also don't understand the repeated claim that the energy distribution over frequencies is arbitrary and meaningless for wavelet convolution. Morlet wavelet convolution is simply Gaussian-windowing in the frequency domain and then going back to the time domain via IFFT. It's essentially the same thing as narrow-band temporal filtering, so you would also need to make the claim that the frequency characteristics of a narrowband filtered signal are arbitrary and meaningless. It's also not really different from smoothing out the power spectrum of a (non-tapered) STFFT.

4) To me, the take-home message is that analysis parameters must be carefully selected. If I were on this paper, or if I were a reviewer, I would want to see another figure that shows how wavelet convolution can give the correct result (given proper parameters) and how STFFT can give incorrect results (given poorly selected parameters). As-is, I'm afraid that readers may take the wrong message, which is to blindly trust Welch's method and blindly ignore wavelet convolution.

5) I think it's a straight forward study that STFFT and wavelet can give the same or different results, depending on parameter selection. There is a paper from Bruns that shows this pretty exhaustively, including a comparison with narrowband filtering and the Hilbert transform. I sometimes give this as an exercise when I teach data analysis courses.   

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Mike X Cohen, PhD
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[Demetris Roumis]

Hi Mike,

Thanks for taking the time and for the awesome response! I totally agree with your assessment about the paper. :)

I like the idea of using FWHM to parameterize the wavelets, it is certainly more intuitive than ncycles, although I'm not sure I see understand how it resolves the issue of choosing the upper bound of of the param range.

In your paper's code, you use 800:700ms

fwhm = linspace(.8,.7,nfrex);

, for frequencies 2:25Hz. I understand that 800ms is reasonable for the low end, but I'm curious why 700ms for 25Hz? Did I misunderstand something, and that this was analytically derived?

To give a bit more context, I care about this is because (I think) using too narrow of a gaussian for the higher frequencies would penalize high frequency time-frequency-clusters more than lower frequency time-frequency-clusters during cluster size correction, since the the cluster size distribution is based on the entire time-frequency map. no?

Thanks!

-Demetris

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[Mike X Cohen]

I didn't give a specific recommendation because that is difficult to do. I think it should depend on how much smoothing you think is appropriate, given your data, experiment, hypotheses, etc. And that's really the primary motivation for being able to specify the smoothing in terms of seconds or Hz, rather than number of cycles. I think for many experiments, smoothing in the range of .5-1 second seems reasonable to me.

Your other point is also true -- cluster correction tends to favor lower frequencies, because the blobs in lower frequencies tend to be larger. For 2-25 Hz, I don't think this should be a significant concern. 

Mike

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Mike X Cohen, PhD
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