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Which is why the Nyquist sampling constraint does not assume a sinusoid, nor is it expressed in terms of the fundamental. It is properly expressed in terms of the bandwidth (and not the 3dB bandwidth, nor in terms of the maximum frequency). With a squarewave, even 10x can be insufficient. And with impulses, it's even worse. The Nyquist criterion is really quite straightforward. It's just that many have never bothered to read what Nyquist actually said.
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The sinewave example I gave is an example of "lies we tell to children" to avoid the maths. When I follow that up with a lecture using the proper maths, I point out that a sine occupies zero bandwidth, so Nyquist actually tells us that we could sample it at an arbitrarily low rate without losing any information at all, because a sinewave actually has no information. Then that leads to a revisiting of aliasing, sampling scopes, and compressed sensing, and also sets us up for an extended discussion on Shannon channel capacity. -- Cheers Tom -- Prof. Thomas H. Lee Allen Ctr., Rm. 205 350 Jane Stanford Way Stanford University Stanford, CA 94305-4070 On 11/22/2021 13:15, David C. Partridge wrote:
Any assumption that you are looking at a sine wave is frankly na?ve. |
