[Eeglablist] Units in output of timefreq - wavelet normalization

[Makoto Miyakoshi]

Dear Mike,

Thank you for your input.

> I'll conclude by reiterating that interpreting any "absolute" voltage
value should be avoided whenever possible.

Yes, I agree with you. That's the conclusion I saw when talking to an
EEGLAB developer.

> In fact, total FFT power is the same as total time-domain power, so the
most power you can get from the FFT will be sum(signal.^2), which is a lot
more than what you'd get from any wavelet.

Right, that's the Parseval's theorem.

Makoto



On Wed, Aug 17, 2016 at 11:05 AM, Mike X Cohen <mikexcohen at gmail.com> wrote:

> Hi everyone. I agree with Andreas that normalization is a tricky issue
> and, to some extent, a philosophical one. In general, I recommend against
> any interpretation of "absolute" values, because (1) they depend on a
> variety of uninteresting factors like electrode montage, equipment, filter
> characteristics, and so on, (2) they are entirely incomparable across
> methods. You can compare dB or % change between EEG, MEG, and LFP, but it
> is impossible to compare EEG microvolts with LFP microvolts, MEG teslas,
> change in light fluorescence, etc.
>
> I point this out because I think we have here mainly an academic
> discussion for the vast majority of neuroscience research, particularly for
> any neuroscience researchers that hope to link their findings to other
> pockets of neuroscience regardless of montage, species, decade, etc. That
> said, if there's one thing academics love, it's an academic discussion ;)
> so here are my two cents (the Dutch don't use pennies, so you'll have to
> decide whether to round down to zero or up to .05 euros).
>
> From Andreas' code, you can add the following two lines after "signal,"
> which will make a new signal, a chirp. You can then add colorbars to both
> TF plots to see that the power is accurately reconstructed after max-val
> normalization. The two numbers in variable f are for the start and end
> frequencies of the linear chirp.
>
> f=[25 60];
> signal = sin(2*pi.*linspace(f(1),f(2)*mean(f)/f(2),length(t)).*t)';
>
> The next point concerned the increase in power over frequency. This is a
> feature, not a bug. First of all, it is highly dependent on the number of
> cycles. For example, note that the power in the top-middle plot goes up to
> just over .2. Now change the 'cycles' parameter to 30; the power now goes
> up to around .05. In other words, the horrible linear increase was cut to a
> quarter. A constant number of cycles over a large range of frequencies is a
> poor choice of parameter, and it should come as no surprise that poor
> parameter choices lead to poor results.
>
> So why does this even happen? Particularly with a constant time-domain
> Gaussian width, the wavelet gets wider in the frequency domain with
> increasing frequency. This means that more of the signal is being let
> through the filter. More signal = more power. I do not see how this is an
> artifact, or even a problem. The more of the spectrum you look at, the more
> power you will see. If you want to maximize the power, then use the entire
> spectrum. In fact, total FFT power is the same as total time-domain power,
> so the most power you can get from the FFT will be sum(signal.^2), which is
> a lot more than what you'd get from any wavelet.
>
> In other words, the increase in power with increasing frequency is *not*
> due to increasing frequency; it is due to the increasing width of the
> wavelet in the frequency domain. This seems worse for white noise because
> of the flat spectrum, but it will be less noticeable for real brain
> signals, which have 1/f^c shape (whether EEG is broadband and noisy depends
> very much on the characteristics of the signal one is investigating). And
> again, this also depends on the wavelet width parameter.
>
> I'll conclude by reiterating that interpreting any "absolute" voltage
> value should be avoided whenever possible. Of course, there is always the
> occasional exception, but I think we can all agree that we should focus
> more on effect sizes rather than on arbitrary values. Some kind of baseline
> normalization is almost always best, and really the best way to make sure
> your findings can be compared across the growing span of brain imaging
> techniques in neuroscience.
>
> Mike
>
> --
> Mike X Cohen, PhD
> mikexcohen.com
>
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-- 
Makoto Miyakoshi
Swartz Center for Computational Neuroscience
Institute for Neural Computation, University of California San Diego
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