this post was submitted on 16 Jun 2024
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The Norquist-Shannon rate sampling theorem only asserts that for a given maximum frequency, you only need another other given maximum frequency of sampling to represent it.
It does not say you can “perfectly” reproduce a signal. Only that you can reproduce all fourier components of the signal that are below half your sampling rate in frequency. It perfectly does that, yes.
But the signals that only contain a finite number of frequencies all below a certain maximum frequency are abstractions used in signal theory classes for teaching that theorem, and in engineering to hit a “good enough” target, not a “perfect” target.
Any frequencies bouncing around the room at over 22 kHz are lost at least to something using the 44 kHz sampling format.
TL;DR: Norquist-Shannon lets you completely reproduce signals with finite information in them. But real life sound doesn’t have finite information in it.
It's Nyquist–Shannon. Norquist is taxes.
Also frequencies greater than half the sampling rate aren't lost they fold into lower frequencies unless filtered out.
But if you think it's easiser to capture those room acoustics with analog equipment the non linear amplification and distortion of any analog system is going to change the sound just add much if not more then a good digital system.
So yeah both lose or distort the signal but digital does it in avery predictable way that can be accounted for and it does have a frequency region that it captures precisely. Analog doesn't.
Nyquist, thank you.
If by “fold into” you mean they add noise to and hence distort the readings on the lower frequencies, that’s correct. But that just takes it further from a perfect reproduction.
Frequency folding is the term used in DSP no need for quotes. The Nyquist frequency is commonly referred to as the folding frequency.
And yes frequencies above the Nyquist folding frequency alias into lower frequencies. A simple low pass filter prevents this however.
Properly filtered digital sampling produced a more accurate reproduction of the frequency range with less distortion then an analog signal.
Also I used quotes to refer to your words, not to throw shade at a term’s validity. I use quote marks to quote.
Doesn’t mean the same thing as just randomly surrounding it with quotes in normal use means.
I don’t disagree that there’s noise in analog signals too, limiting their information capacity. But that’s coming from the limitations of our physical implementations’ quality, no?