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> sampling at 44.1 kHz prevents you from accurately preserving e.g. a sine tone at above ~6 kHz

This is mathematically false. A 6kHz or 8kHz or 10kHz or 20kHz signal absolutely can be perfectly preserved with a 44.1kHz sample rate. Not just kind of preserved, but perfectly preserved.




It's perfectly preserved only if your samples are perfect. Imagine instead that we used 4-bit samples. The results would be obviously garbage. 8-bit would be better. 16-bit is better still. But it isn't perfect.


Increasing the bitrate lowers the noise floor. But that 6 or 8kHz signal is still there.

8:43 in the second video, he goes in to showing what increasing the bit depth gets you.

https://xiph.org/video/vid2.shtml


I doesn't look like you understand what sampling is, and how reconstruction filters in DACs work. Your statement is true for some waveforms, depending on their frequency, due to the use of reconstruction filters on the output, but it's not true for any signal and the problem becomes more apparent the higher the frequency of the waveform.


Reconstruction filters in DACs are analog low-pass filters. They don't do a linear interpolation between samples.


You explicitly said a 6 kHz sine wave. Which is pretty much the textbook example of a waveform and frequency which would work perfectly.

Maybe you wanted to say square wave?


If I'm understanding you correctly, you're saying that while a perfect sinc interpolation reconstruction would allow you to capture up to 44.1/2 kHz, in practice since we're limited to FIR reconstruction filters we can't actually get that high? If so it seems like a fair point, although I'd imagine they'd be better than 6khz?

There's also the issue of the input signal not being band-limited which is necessarily true for real world signals given that you sample for a finite duration.


Input signals are ALWAYS band limited for digital systems. If you don't do this and you work for any company designing such circuitry, you'd be fired.


There's no such thing as a finite support band-limited signal.




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