You've misunderstood something about Nyquist. A sample rate of, say, 44KHz, will capture ALL information below 22KHz and recreate it perfectly.
There are of course implementation details to consider, for example you probably want to have a steep filter so you don't wind up with aliasing artifacts from content above 22KHz. However it's important to understand: Nyquist isn't an approximation. If your signal is below one half the sample rate, it will be recreated with no signal lost.
> In particular, this minimal frequency is twice the bandwitdh of the function.
Careful, this is misleading.
If the peaks of the frequency align with your samples, you'll get the full bandwidth.
If the 0-crossings align with your samples, you'll miss the frequency.
These are why people swear by things like HD audio, SACD/DSD, even though "you can't hear over 20khz"
You've misunderstood something about Nyquist. A sample rate of, say, 44KHz, will capture ALL information below 22KHz and recreate it perfectly.
There are of course implementation details to consider, for example you probably want to have a steep filter so you don't wind up with aliasing artifacts from content above 22KHz. However it's important to understand: Nyquist isn't an approximation. If your signal is below one half the sample rate, it will be recreated with no signal lost.
I was just about to post something saying similar. If I had to guess,
>If the 0-crossings align with your samples, you'll miss the frequency.
This is where the issue is. This isn’t possible with more than double the sampling rate.
It can only happen with a source exactly at N/2 and correlated with your sampling clock. That doesn't happen in the real world for audio.
Yep, that's why people do things like 44kHz sampling instead of 40kHz.
How bad is it around the frequencies I can hear as a 30-something?
Off topic, this thesis has one of the most concise and straightforward acknowledgments section I saw.