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@ Mike Dilger
2025-02-21 08:07:56
This image shows the same frequency (exactly half the sampling rate) represented by the samples at the dots. All three of those waves produce the same set of samples. These are called aliases. They all have the same frequency. But they don't have the same amplitude (or phase). The phase you can't hear. But the amplitude does matter.
https://en.wikipedia.org/wiki/File:CriticalFrequencyAliasing.svg
So yes there is something a bit wrong with the interpretation of the Nyquist-Shannon sampling theorem that posits that if you use 2x the frequency you perfectly represent everything below frequency x.
Wikipedia hand waves this away https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem by pointing at the strict inequality. But I don't think that's enough.
Take for example a frequenty very slightly less than x, sampled at 2x. Those samples would produce a very low frequency pattern. But the sampled wave is a very high frequency pattern. You would be unable to distinguish between the high frequency and it's low frequency reflection in this sample set.
So my instinct is that you are right. But also I know what everybody in the field says, that we are wrong. I'll just put that aside as an "hmm, interesting" until I get some better data or explanation as to why our observations here somehow don't matter.