[StrangeDoctor]

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.

[kevin_thibedeau]

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.

[mlyle]

Anything close to N/2 is going to have varying magnitude that requires filtering and likely oversampling to remove.

How close to the Nyquist bandwidth you can get depends upon the quality of your filtering.

44.1KHz is a reasonable compromise for a 20KHz passband. 48KHz is arguably better now that bits are cheap-- get a sliver more than 20KHz and be less demanding on your filter. Garbage has to be way up above 28KHz before it starts to fold over into the audible region, too.

[Sesse__]

> Garbage has to be way up above 28KHz before it starts to fold over into the audible region, too.

You brick-wall everything at 20 kHz (with an analogue filter) before you sample it; that's part of the CD standard, and generally also what all other digital CD-quality audio assumes. This ensures there simply is no 28 kHz garbage to fold. The stuff between 20 and 28 in your reconstructed signal then is a known-silent guard band, where your filter is free to do whatever it wants—which in turn means that you can design it only for maximum flatness (and ideally, zero phase) below 20 kHz and maximum dampening above 28 kHz (where you will be seeing the start of your signal's mirror image after digital-to-audio conversion), not worrying about the 20–28 kHz region.

[mlyle]

Your comment is mutually contradictory-- what is it, a brick wall (impossible) analog filter or a more gentle rolloff as things fold over?

What you really do, these days, is you sample at a higher frequency; you can have an exceptionally gentle analog filter (which will help you make it linear, too). E.g. if you sample at 96KHz, you just need to roll to near zero by 75KHz. Then you can digitally downsample/decimate to 44.1KHz or 48KHz.

Also note for CD audio, it's more like 24KHz where you get worried, not 28KHz.

[Sesse__]

You're mixing up the two filters. The pre-sample filter (before ADC) is defined to be a brickwall (of course impossible in practice, so in reality, it will have to start going off a bit before 20 kHz); the reconstruction filter (after DAC) has a roll-off.

[mlyle]

I've not been talking about the reconstruction filter at all during any step of this discussion. Reading your comment more carefully, it seems you were trying to.

I'm saying that if you oversample, it's easier to get appropriate rejection from your pre-sampling filter and it's easier to make it appropriately flat as well.

E.g. sample at 384KHz; you need to reject stuff over 360KHz. You probably have negligible energy up there to begin with. A 3rd-order filter with -3dB at 30KHz might get the job done. It's pretty easy to make this flat in phase and amplitude up to 20KHz, and things like capacitor nonlinearity are much less of a concern.

In turn, filtering down to 20KHz and rejecting from 22050 and up is easy in the digital domain. 512 taps gets me a filter flat to 0.15dB up to 20KHz and >63dB rejection over 22KHz.

My point was, this is a little better at 48KHz, because we can choose to e.g. pass 21KHz and have a wider guard band (14% vs 10%). With 384 taps, numbers are more like flat to 0.1dB and -67dB, benefitting both from the wider guard band and 48KHz being a factor of 384KHz.

[marcosdumay]

Yep, that's why people do things like 44kHz sampling instead of 40kHz.

[Sesse__]

No, 44 kHz is because you want to reconstruct the (20 kHz) bandlimited signal and it's (much) easier to realize such a filter if you have a bit of a transition band.