Why record higher than 44.1 khz?

[Farview]

The theoretical brickwall will be after 22050hz, but the wave is 22000hz, so it won´t be affected by that brickwall. Which means I don´t need to take it into account because it cuts only all frequencies higher and those are not present in sine wave.

The brick wall would have to be before.

You say the 22000hz won´t be there, or the 50hz?

The 50hz is caused by the interaction between the 22k and the 44.1k, if you take away the 22k the 50hz won't happen.

I understand this that if I sample for example a 22000hz wave with 44.1khz sampling, the samples will determine the 22k wave.
But when I look at the samples (which as I remember won´t look like a 22khz sine wave), and sample the exact wave like the one I can see, (in the way that I create a signal which will produce the same samples), I will obtain the same series of samples as above.
That means to me, that the function is not really determined by the samples, because I have two different input waves, which produce the same samples.

Where is the second wave form? I'm not getting what you are doing. How are you 'looking' at the samples?

The digital-analog conversion doesn´t play any role, because the theorem says that the original function is determined by the samples, and I have shown that there exist at least two different input waveforms that produce the same samples. Therefore the function cannot be determined by the samples.

How are they different? They would have to have a different amplitude or frequency. In which case, they would create different samples.

 

[SouthSIDE Glen]

The lack of a brick wall is what it's all about, kubeek. Nyquist as described applies strictly to a bandwidth-limited signal. But because there is no brick wall at 44.1, but rather a soft LP filter, the signal is not bandwidth limited. Therefore the aliasing DOES show up. Which is why DACs have anti-aliasing filtering and is why the sample rate is higher than the pure Nyquist frequency.

Circuit design may not affect the bit values at all once in digital, but circuit design DOES matter in the conversion itself in either direction. Nyquist is strictly bandwidth limited; i.e. it states that a 40kHz sample rate will losslessly and accurately reproduce a 20kHz signal specifically and only when the signal has absolutely zero components above 20kHz. But because our analog filtering cannot physically brick wall at 20kHz, i.e. we cannot absolutely guarantee our signal is bandwidth limited to 20kHz, we cannot physically guarantee a design that can deliver the promised Nyquist accuracy at the Nyquist frequency.

Which is why that part about sampling at higher than Nyquist is a very important factor, and one which your test is ignoring, also. What you need to be looking at is not a 22kHz signal but rather a 20kHz signal. The sample rate is 44.1 instead of 40 very much because of the kind of thing you are seeing. The A/D converter through which that 22kHz signal passed is not *meant* to accurately reproduce 22kHz. It is meant/designed to deliver up to ~20kHz without such artifacting; anything above is technically out of spec.

G.

 

[Farview]

we really don't even have to get into all this. If Nyquist didn't work, there would be no such thing as digital audio. There is, so it does.