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<p class="MsoNormal">All:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I would add that the <u>reason</u> aliasing still occurs is that real-world filters are not perfect and do not have an actual step-function at the nominal stop-band frequency. In other words, they still let some higher frequencies through.
To properly sample these you need a higher sample rate than the theoretical Nyquist rate.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">You really need to know the actual analog filter roll-off when choosing the optimal sampling rate, as well as the inherent noise in the electronics. Presumably the equipment designer will have taken this into consideration.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Another reason to oversample is to make the resulting reconstruction look more pleasing to the eye. If you sample a pure sine wave strictly at the Nyquist rate, it will look triangular. This can be fixed by the proper reconstruction technique,
which virtually no one does as it involves additional computation involving multiplication with sinc functions.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">-Jeff Eriksen<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><b>From:</b> eeglablist <eeglablist-bounces@sccn.ucsd.edu> <b>
On Behalf Of </b>Michael D. Nunez<br>
<b>Sent:</b> Monday, March 4, 2019 9:05 AM<br>
<b>To:</b> Eric Rawls <elrawls@email.uark.edu><br>
<b>Cc:</b> eeglablist <eeglablist@sccn.ucsd.edu><br>
<b>Subject:</b> [EXTERNAL] Re: [Eeglablist] Nyquist, downsampling, and EEG<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="color:red">This email originated from outside of Legacy Health. Please use CAUTION when clicking on links or opening documents.</span>
<o:p></o:p></p>
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<p class="MsoNormal">Hey Eric, <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">There is still aliasing that can occur past the Nyquist rate. That's why an Engineer's Nyquist of 2.5 the max desired frequency is often used. Also we may want to accurately record artifact above 50 Hz to better remove that artifact. <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Furthermore there is no real cost to having large sampling rates, besides initial file size, in EEG experiments where the analysis is performed offline. We can always downsample offline. In some online Brain-Computer Interfaces (BCIs),
the sample rate will be a concern. <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt">Michael<o:p></o:p></p>
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<p class="MsoNormal">On Sun, Mar 3, 2019, 23:32 Eric Rawls <<a href="mailto:elrawls@email.uark.edu" target="_blank">elrawls@email.uark.edu</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal">Hi list, I have a short, more theoretically designed question.
<o:p></o:p></p>
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<p class="MsoNormal">Typical ERP studies will apply a filter around 50 Hz to remove frequencies above line noise. <o:p></o:p></p>
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<p class="MsoNormal">Doesn't this mean that for any data filtered this way the highest reasonable sampling rate is 50*2=100 Hz? <o:p></o:p></p>
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<p class="MsoNormal">So why does we all use 500, or even 1000 Hz, when sampling EEG signals?<o:p></o:p></p>
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<p class="MsoNormal">Does this lower limit on the sampling rate need to increase for phase based analyses etc?<o:p></o:p></p>
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<p class="MsoNormal">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?<o:p></o:p></p>
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<p class="MsoNormal">Thanks for the discussion<o:p></o:p></p>
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<p class="MsoNormal">Eric Rawls, M.S.<o:p></o:p></p>
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<p class="MsoNormal">Graduate Research Assistant & Instructor<o:p></o:p></p>
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<p class="MsoNormal">Department of Psychological Sciences<o:p></o:p></p>
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<p class="MsoNormal">University of Arkansas<o:p></o:p></p>
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<p class="MsoNormal">_______________________________________________<br>
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