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[krasse]

I know that the sampling theorem tells us that we can represent frequencies up to half of the sampling rate and up till now I have accepted this as a fact.

But if you take the phase into consideration then it seems to be a much more difficult problem to represent the signal correctly and not cause any artifacts when the phase is modulated (which is just normal when using filters with changing frequencies etc).

Suppose for example that you sample a 20050 Hz sine wave at 40100 Hz. Then you get two samples for each period. The extreme cases are that you sample it at the peaks or at the zero-crossings which in the first case gives you a very nice representation and in the second one just a flat line.

So increasing the sampling rate seems to do wonder in this case since you can in both of those extreme cases get a good result by simply doubling the sampling rate!

It gets even worse if you modulate the phase of the signal in the 44100 Hz sampling rate! Then the signal goes from a clear 20050 Hz representation into zero at the rate of the phase, which is not going to happen when you increase the sampling rate.

So, how do I continue to work with audio after this? Should I try to use a much higher sampling rate during processing, or is it something I am missing here?

[Pishtaco]

I think the theorem is that you can construct frequencies less than half the sampling rate (so not including exactly half the sampling rate, as your example shows).

This looks like a good account of it: http://www.wescottdesign.com/articles/Sampling/sampling.pdf

[krasse]

I think the theorem is that you can construct frequencies less than half the sampling rate (so not including exactly half the sampling rate, as your example shows).

This looks like a good account of it: http://www.wescottdesign.com/articles/Sampling/sampling.pdf

Thanks! That was really useful. I now understand that there is a difference in representing frequences in samples and gathering info with sampling.