Quote:
Originally Posted by TweakHead
Correct me if I'm wrong here: but the number of points within a second is determined by our choice of sample rate, right?
|
For digital time domain signal, yes. For frequency domain signal, the amount of points depend on the length of the signal, the usable bandwidth on the sample rate. Analog signal is however continuous in time domain, we can't ever hear a digital signal...
Quote:
Originally Posted by TweakHead
so this would give us 44100 points a second, for example. If you divide this number by 30,5 you get 1445,9016393442623 points per cycle, right?
|
I didn't do the math, but I have no problems believing that what you are saying is correct. (but it is irrelevant).
Quote:
Originally Posted by TweakHead
While for 30Hz you'd have 1470 points. For 31Hz it would be 1445,9016393442623 points. Of course the problem is there's nothing but whole numbers in there. So you're saying that we need more time so that there's enough points to get to a whole number and thus completing a perfect cycle, I think. And I'm saying that the mere phase difference should be enough to distinguish these pitches even within such a short time frame. That the time duration of the cycles is enough to determine pitch with precision, provided there's at least one complete cycle (???).
|
No, this is not at all what I am saying. The limitations I am describing applies to analog domain and infinite sample rate digital signals as well. You can't have a 30.5hz sine wave in one second time window, be it analog, digital, infinite sample rate or whatever. The sine just won't fit in the window! A signal can only consist of sine waves that fit in the window (because by definition those are sine waves, other waves are, not sine waves - meaning that they are composed of many different sine waves)...
What you are describing is simply that periodic signals in analog domain may not be periodic in the digital domain in the sense that the sample points would repeat themselves periodically as the analog wave does. To get around this some of the digital cycles are going to have more points, this is unimportant, because they will still fit into the one second window perfectly. However, this does mean we can't take a fourier transform of a 1.0000001 second signal, because the FFT size of 44100.1 samples does not exist. So there is that type of restriction with digital, which can be overcome with oversampling though.