Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
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Re: Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
#2Many brilliant points. Particularly about Bessel filters instead of Butterworth. And also about lowering Fc and increasing Fs, rather than increasing order. And also about considering time domain as well as frequency domain.
The dense interview question I use to assess this area of knowledge: "How do you choose the stopband attenuation of a filter?" You can assess a lot from the interviewee's response. Stopband attenuation, with respective to the input signal magnitude at the stopband frequency, or start of the stopband, is the most relevant term for determining the magnitude of noise in the sampled signal. And that is the upper bound on the performance of the downstream algorithm.
Re: Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
#3If you're thinking "The highest rate I need my signal to be able to replicate is X, so I should set my sampling rate to 2X," then you're wrong and this article gives several reasons why.
As far as I can tell, though, it doesn't mention what may be the most important reason (especially to the folks here at hackernews): resampling and processing.
This is why professional grade audio processing operates at a sample rate many multiples higher than human hearing. It's not because of the quality difference between, say, 192 and 96 kHz, but rather if you're resampling or iterating a process dozens of times at those rates, eventually artifacts will form and make their way into the range of human hearing (20 kHz).
Re: Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
#4If you're thinking "The highest rate I need my signal to be able to replicate is X, so I should set my sampling rate to 2X," then you're wrong and this article gives several reasons why. As far as I can tell, though, it doesn't mention what may be the most important reason (especially to the folks here at hackernews): resampling and processing. This is why professional grade audio processing operates at a sample rate…
Yeah, a lot of people think “Nyquist” is a synonym for 2 and stop thinking further.
Re: Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
#5It’s interesting to me how frequently people will talk about sampling performance profilers and not know about Nyquist.
Given a CPU runs at many GHz but SW sampling profilers run at ~1 or even maximum 10khz, it’s really hard to write software if you’re targeting processing at MHz rates.
Re: Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
#6If you're thinking "The highest rate I need my signal to be able to replicate is X, so I should set my sampling rate to 2X," then you're wrong and this article gives several reasons why. As far as I can tell, though, it doesn't mention what may be the most important reason (especially to the folks here at hackernews): resampling and processing. This is why professional grade audio processing operates at a sample rate…
Not just eventually: many effects, such as basically any non-linear mapping like a distortion, will create overtones that will immediately alias down if you are not oversampling. You either need to use some DSP tricks or oversample (usually a mix of both) to avoid this happening, which often happens in just one step of an effects chain.
Re: Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
#7I have referred so many people to this paper over the years. It does a great job of dispelling a lot of misunderstandings people have about Nyquist's theorem.
Re: Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
#8It’s interesting to me how frequently people will talk about sampling performance profilers and not know about Nyquist. Given a CPU runs at many GHz but SW sampling profilers run at ~1 or even maximum 10khz, it’s really hard to write software if you’re targeting processing at MHz rates.
I'm not sure what you mean here, but I would say that sampling profilers are a good example of Nyquist applied correctly for the most part: your signal (the distribution of where your software is spending its time) is likely to have an extremely low bandwidth (as in, it's basically static), so why try to sample super rapidly? It's much more of a question of whether you get enough samples to represent that distribution accurately, not how quickly you get those samples.
Re: Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
#9If you're thinking "The highest rate I need my signal to be able to replicate is X, so I should set my sampling rate to 2X," then you're wrong and this article gives several reasons why. As far as I can tell, though, it doesn't mention what may be the most important reason (especially to the folks here at hackernews): resampling and processing. This is why professional grade audio processing operates at a sample rate…
You’re right, but I fear this idea has become prevalent in audiophile communities where they only want to listen to files that are 96kHz or higher.
In my opinion, having a high sample rate only really matters during the production phase and does not have a noticeable effect on the final form factor. If the producer uses high sample rate during the creation process, I see no reason why the listener would care if the file they’re listening to is higher than even 44.1kHz unless they are planning on using it for their own production.
Re: Sampling: What Nyquist didn't say, and what to do about it (2018) [pdf]
#10If you're thinking "The highest rate I need my signal to be able to replicate is X, so I should set my sampling rate to 2X," then you're wrong and this article gives several reasons why. As far as I can tell, though, it doesn't mention what may be the most important reason (especially to the folks here at hackernews): resampling and processing. This is why professional grade audio processing operates at a sample rate…
Not just eventually: many effects, such as basically any non-linear mapping like a distortion, will create overtones that will immediately alias down if you are not oversampling. You either need to use some DSP tricks or oversample (usually a mix of both) to avoid this happening, which often happens in just one step of an effects chain.
Even the term "oversampling" implies that sampling beyond Nyquist rate is excessive. I think you would agree that one is not being excessive. It is necessary to sample well beyond accepted "Nyquist rate" in order to reconstruct the signal.