Great video! I came here from Technology Connect’s video on Nyquist-Shannon, I was struggling to follow so I came here for a dedicated lesson on the Nyquist frequency, and you explained it amazingly. Thank you!
@1.18 On the other hand if f0 = 2fs you might not obtain sample values that properly represent the signal. Suppose that the samples are taken at the zero crossing points of the sinusoid. The minimum sampling frequency is greater than (and not equal to) the highest frequency component in the signal. Nyquist states this but is often misquoted.
I wish that given the formula f_0 = x*f_s, we referred to x more than the sample rate, as it is what really is useful in these equations and understanding the nyquist theorem. Additionally, it's basically why we have sample rates above twice the human hearing limit.
The Nyquist frequency (= half the sampling rate) is the highest frequency you can hope to observe in the data. If even higher frequencies occur in the data, the process of sampling the data will alias those true high frequencies to lower frequencies.
In this video, the black curve is the "true brain signal". That's what we'd like to observe. But we never get to. Instead, we observe a sampling of the signal (the green, yellow, or red dots). Sampling too slowly can cause problems.
2:20 Horrifying? Why is aliasing always described as something horrible and something that absolutely has to be avoided? Let me circumvent any answer by inviting you to Google Sub-Nyquist sampling! As long as the bandwith of the sampled signal doesn't exceed 1/2fs, it's an acceptable sampling method to sample in a higher Nyquist zone. And that's precisely what Nyquist said, it literally says bandlimited signal. Not "maximum frequency component contained in the signal"!.
Want to know more? Check out our book, mitpress.mit.edu/books/case-studies-neural-data-analysis and/or our website with examples in Python, mark-kramer.github.io/Case-Studies-Python/intro
