4 ms·

> these get reconstructed to pure sine waves by the AD/DA converter That's not at all how DACs work. They create a stepped voltage output in some way, which is

> these get reconstructed to pure sine waves by the AD/DA converter That's not at all how DACs work. They create a stepped voltage output in some way, which is then filtered to remove the steppiness. Yes, if you're decoding a sequence of values that represent a sine wave, you'll probably end up with something functionally indistinguishable from a sine wave at the end, but 'reconstructed to pure sine waves' is nonsense. Agree with everything else though.

mannykannot 4y ago
It takes a familiarity with the Fourier transform to appreciate what jrajav is claiming. The digitization introduces a high-frequency fundamental, harmonics of the fundamental, and additional artifacts that are at the sums and differences of these sampling frequencies and those in the signal. So long as the input is filtered so that it contains nothing above the half the sampling frequency (the Nyquist frequency), the artifacts introduced by digitization are all above the filter's cutoff frequency and can be removed from the reconstructed signal. At that point, if the original signal was a pure sine wave, then so is the reconstruction. The technology is not perfect, of course - the digitization and its reversal is not arbitrarily accurate and the pure step filter does not exist - but, in practice, with a suitably high sampling rate, the infidelities can be reduced to the point where they are insignificant in comparison to those introduced by other parts of the process. It is pointless to talk here about the digitization separately from the filtering, which is an essential part of the process, and it is pointless to argue that the filtered signal is not the original when the difference is undetectable by anyone. And if we were to be pedantic, then every signal is identical to a collection of one or more pure sine waves (possibly phase-shifted). Jrajav's statement is not nonsense.
- jrajav 4y ago
  Indeed, the nature of the fourier transform is what allows for the signal to be perfectly reconstructed in theory for frequencies below Nyquist. More practically, it's not only filtering but also the slewing nature of both the analog part of a DAC as well as the physical speakers themselves. I only brought this up specifically because I've seen more than a few times in "Analog is better" articles the 'stair step' representation of a jagged digital waveform, which is itself total nonsense.
  - camtarn 4y ago
    I'm very familiar with the basic details of the Fourier Transform, Nyquist Theorem, etc etc. I was taught how to build a DAC from discrete components in University, and I've read up on the multiple types of DAC. And I still disagree over this minor point of wording - I still don't think it makes any sense. But honestly, it really doesn't matter. You clearly know what you're talking about, wording or not, and I understand your argument and think it's sound, so no further nitpicking from me :)
    - mannykannot 4y ago
      You are, of course, entitled to your own opinion - even though you apparently know all the relevant facts!

mannykannot 4y ago

It takes a familiarity with the Fourier transform to appreciate what jrajav is claiming. The digitization introduces a high-frequency fundamental, harmonics of the fundamental, and additional artifacts that are at the sums and differences of these sampling frequencies and those in the signal. So long as the input is filtered so that it contains nothing above the half the sampling frequency (the Nyquist frequency), the artifacts introduced by digitization are all above the filter's cutoff frequency and can be removed from the reconstructed signal. At that point, if the original signal was a pure sine wave, then so is the reconstruction. The technology is not perfect, of course - the digitization and its reversal is not arbitrarily accurate and the pure step filter does not exist - but, in practice, with a suitably high sampling rate, the infidelities can be reduced to the point where they are insignificant in comparison to those introduced by other parts of the process. It is pointless to talk here about the digitization separately from the filtering, which is an essential part of the process, and it is pointless to argue that the filtered signal is not the original when the difference is undetectable by anyone. And if we were to be pedantic, then every signal is identical to a collection of one or more pure sine waves (possibly phase-shifted). Jrajav's statement is not nonsense.

jrajav 4y ago
Indeed, the nature of the fourier transform is what allows for the signal to be perfectly reconstructed in theory for frequencies below Nyquist. More practically, it's not only filtering but also the slewing nature of both the analog part of a DAC as well as the physical speakers themselves. I only brought this up specifically because I've seen more than a few times in "Analog is better" articles the 'stair step' representation of a jagged digital waveform, which is itself total nonsense.
- camtarn 4y ago
  I'm very familiar with the basic details of the Fourier Transform, Nyquist Theorem, etc etc. I was taught how to build a DAC from discrete components in University, and I've read up on the multiple types of DAC. And I still disagree over this minor point of wording - I still don't think it makes any sense. But honestly, it really doesn't matter. You clearly know what you're talking about, wording or not, and I understand your argument and think it's sound, so no further nitpicking from me :)
  - mannykannot 4y ago
    You are, of course, entitled to your own opinion - even though you apparently know all the relevant facts!