[Eeglablist] Units in output of timefreq - wavelet normalization

[Mike X Cohen]

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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://sccn.ucsd.edu/pipermail/eeglablist/attachments/20160817/7c8001c2/attachment.html>