<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<p>Dear Eric,</p>
<p>Did you mean the "lowest reasonable sampling rate"? Nyquist
theorem says that to represent frequency Fn, you need at least
twice as much sampling rate Fs=2*Fn - this is a minimum and in
practice we like to sample much more (though we try to keep it
reasonable on the other side, each time you double the sampling
rate, you add to computation time and file storage burden). When
there isn't any further specifics, I personally use a sampling
rate at 10 times the fastest frequency of interest (Ffoi) I am
interested in quantifying properly. So if my Ffoi is 100Hz, I'd
have a Fs of 1,000Hz (and therefore a Fn of 500Hz, and for good
measure, see below for clarification, an analog filter at 200Hz).
<br>
</p>
<p>You might imagine (or draw on paper) the undulation of a sine
function. If you get only two points to represent each cycle as
per the minima of the Nyquist theorem (sample 2 evenly spaced dots
per cycle, starting from a random timepoint, and connect with with
a ruler), then you have a rough, angular, poor-looking
representation of your nice and smooth sin function (one point
somewhere in the up side, one in the down side). That bad-looking
data is what goes in your digital file of an EEG. Amplitude is
quite distorted. Frequency probably also. Phase, as you suggest,
will be hard to accurately estimate. In the singular case that
you'd have the sampling rate Fs exactly at twice the Nyquist, and
you'd start sampling at a zero crossing, you'd even manage to
obtain a perfectly flat signal, as if your wave did not even
undulate. So the more you add points (sampling rate Fs) to
discretely sample your cycles, 2 at a very bare minimum, maybe at
least 5 or 10, the nicer looking your data. <br>
</p>
<p>Further, to ensure that the discrete sampling of the signal does
not betray you (improperly showing as slow frequencies brainwaves
that were initially faster than Fn), we always apply, at recording
and as an important safety measure, an analog lowpass filter
(ideally at good distance from the Nyquist frequency Fn, say, 2
times slower than the Nyquist frequency Fn). This is to be sure
that all faster-than-Nyquist frequencies are suppressed and
therefore unable to be misrepresented. Further digital filter
might happen, the filter you talk about might be one, perhaps
aimed at suppressing line noise (50Hz Europe, 60Hz US), in the
event that the recording would carry plenty of it and you would
not have enough epochs to cancel it out. <br>
</p>
<p>Now, two more questions on the heels of this are:</p>
<p>-what is the fastest frequency that is time-locked and worthy of
your effort? This question depends on the specific of your
research, and differs whether you work in a discovery-based or
confirmatory paradigm. Gamma is certainly not a rare occurrence,
you might also look in the literature of the Auditory Brainstem
Responses: those people try to capture early stages of auditory
processing, they usually have to sample at 20,000Hz to get a good
handle on those multiple waves developing in the first 10
milliseconds after auditory event.</p>
<p>-how good is your syncing between the subject's brainwaves and a
digital tag reporting on the time of occurrence of the stimulus?
If you have quite a jitter there (your computer program not being
too good at telling your EEG system when the event happened), then
your efforts to catch faster time-locked components will likely
not be productive, which is why many people might settle for
parameters with {low sampling rate; low analog filter}.</p>
<p><br>
</p>
<p>I try to summarize, if you suspect some interesting stuff in the
fast frequencies, that would be time-locked to a stimulus, if you
have a really good computer program for administration of those
stimuli, then you go for a much higher sampling rate than 100Hz.
If you have restrictions on any of the above, then, you can settle
at a more modest sampling rate. 100Hz though, unless needed for
other constraints, seems quite low.<br>
</p>
<p>I hope this helps, with kind regards,</p>
<p>Emmanuelle Tognoli - Center for Complex Systems and Brain
Sciences<br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 3/3/2019 12:07 PM, Eric Rawls wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAHbtrJ+5Hg7jyy26MP2DORWp=K_zwNG_BByZyBW6d657ctjOjQ@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="ltr">Hi list, I have a short, more theoretically
designed question.
<div>Typical ERP studies will apply a filter around 50 Hz to
remove frequencies above line noise. </div>
<div>Doesn't this mean that for any data filtered this way the
highest reasonable sampling rate is 50*2=100 Hz? </div>
<div>So why does we all use 500, or even 1000 Hz, when sampling
EEG signals?</div>
<div>Does this lower limit on the sampling rate need to increase
for phase based analyses etc?</div>
<div>I've been curious about this for a while and wanted to open
it up to a group of experts. Why do we sample above the
Nyquist rate in our EEG experiments?</div>
<div>Thanks for the discussion</div>
<div>Eric Rawls, M.S.</div>
<div>Graduate Research Assistant & Instructor</div>
<div>Department of Psychological Sciences</div>
<div>University of Arkansas</div>
</div>
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<pre class="moz-quote-pre" wrap="">_______________________________________________
Eeglablist page: <a class="moz-txt-link-freetext" href="http://sccn.ucsd.edu/eeglab/eeglabmail.html">http://sccn.ucsd.edu/eeglab/eeglabmail.html</a>
To unsubscribe, send an empty email to <a class="moz-txt-link-abbreviated" href="mailto:eeglablist-unsubscribe@sccn.ucsd.edu">eeglablist-unsubscribe@sccn.ucsd.edu</a>
For digest mode, send an email with the subject "set digest mime" to <a class="moz-txt-link-abbreviated" href="mailto:eeglablist-request@sccn.ucsd.edu">eeglablist-request@sccn.ucsd.edu</a></pre>
</blockquote>
</body>
</html>