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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

> 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.

masfuerte 3y ago
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.
- vel0city 3y ago
  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 https://xiph.org/video/vid2.shtml
daneel_w 3y ago
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.
- deleted 3y ago
  [deleted]
- krackers 3y ago
  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.
  - rplst8 3y ago
    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.
    - krackers 3y ago
      There's no such thing as a finite support band-limited signal.
- deleted 3y ago
  [deleted]
- baobrien 3y ago
  Reconstruction filters in DACs are analog low-pass filters. They don't do a linear interpolation between samples.
- steve1977 3y ago
  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?

masfuerte 3y ago

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.

vel0city 3y ago
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 https://xiph.org/video/vid2.shtml

daneel_w 3y ago

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.

deleted 3y ago
[deleted]
krackers 3y ago
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.
- rplst8 3y ago
  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.
  - krackers 3y ago
    There's no such thing as a finite support band-limited signal.
deleted 3y ago
[deleted]
baobrien 3y ago
Reconstruction filters in DACs are analog low-pass filters. They don't do a linear interpolation between samples.
steve1977 3y ago
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?