Saurav
Senior HTF Member
- Joined
- Feb 15, 2001
- Messages
- 2,174
Back in college, I know I studied and made it a point to understand Nyquist's theorem and the proof behind it. However, I don't remember any of that now.
but if my assumption above is right (that sampling frequency has little to do with the frequency of the sound being reproduced)
If you believe Nyquist's theorem (which AFAIK most of the scientific community does), then your assumption is wrong - the sampling frequency has everything to do with the highest frequency that can be produced. Or more accurately, the highest frequency that can be recorded. It's possible that a system chooses to record up to a certain frequency, but play back only up to 20 KHz, but that doesn't make sense - why record information that isn't being used?
So, there's two ways to look at this - first, question Nyquist's theorem in the first place. If he is wrong, then 48/96 KHz makes perfect sense - take more samples to get a more accurate reproduction. This is intuitively right - more frequent samples must obviously lead to a smoother output, right? However, Nyquist did prove, mathematically, that you don't need to sample any higher than 2x the highest frequency. Maybe his proof was in error... I cannot make a judgement on that.
The other way to look at this is that human hearing does respond to frequencies above 20 KHz. That would explain the benefits of a higher sampling frequency too, except for one catch - most modern speakers (and amps too, sometimes) do not go much beyond 20 KHz, so that raises the same question as above, what's the point of recording information that you cannot play back.
I also remember something from college called "Causal Filters" - the idea was that most of the math done with filters is valid for time values ranging from negative to positive infinity. However, no filter produces output from the beginning till the end of time - a filter can only produce output when an input is applied to it. I don't remember quite how this was handled in the math, but I wonder if something like this could affect Nyquist's theorem. That is to say, the theorem is valid if you're sampling a signal which extends backwards and forwards in time infinitely, but since no real signal does that, maybe that affects the theorem in some way. This is just a guess.