4 ms·

So you could claim to be able to reconstruct output of that filter. Which still is not the case — you cannot have signal to be both aperiodic and band-limited:

by 112233 4y ago

So you could claim to be able to reconstruct output of that filter. Which still is not the case — you cannot have signal to be both aperiodic and band-limited: either in time domain or in frequency domain signal will be periodic. So no real (that is, finite) signal satisfies requirements of Nyquist theorem. Not only that, your DAC needs to have infinite lookahead to reproduce the same input that was passed to ADC.

dreamcompiler 4y ago
Okay you're saying mathematical perfection is not achievable in the real world. Fine. It doesn't matter. What matters is that with a digital signal processing chain you essentially have a knob you can turn to approach mathematical perfection as closely as you wish, at least until you reach the point where the inherent limitations of your analog components begin to matter. And that point is far, far beyond where human hearing can tell the difference. But with analog signal processing you reach the limitations of analog componentry much quicker, while you are still well within the noticeable range of some humans to tell the difference. This is because the entire chain is analog and thus no part of the chain is immune to information loss or added noise. With a digital chain, only the ADC and DAC stages require high quality analog componentry. Everything in between is pure math. Neither process is capable of overall mathematical perfection, but digital can approach it much more closely than analog.
- 112233 4y ago
  Absolutely agree. Even more, once you are in digital, you can have actual mathematical perfection, that is reproducible and does not degrade with time. I just seem to take issue when Nyquist is getting inwoked. That is a purely mathematical result. It is sufficient (and I think required, too) to plug source into ADC+DAC, measure the output and show that the difference is insignificant. And much less than, say, with tape.

by 112233 4y ago

dreamcompiler 4y ago

Okay you're saying mathematical perfection is not achievable in the real world. Fine. It doesn't matter. What matters is that with a digital signal processing chain you essentially have a knob you can turn to approach mathematical perfection as closely as you wish, at least until you reach the point where the inherent limitations of your analog components begin to matter. And that point is far, far beyond where human hearing can tell the difference. But with analog signal processing you reach the limitations of analog componentry much quicker, while you are still well within the noticeable range of some humans to tell the difference. This is because the entire chain is analog and thus no part of the chain is immune to information loss or added noise. With a digital chain, only the ADC and DAC stages require high quality analog componentry. Everything in between is pure math. Neither process is capable of overall mathematical perfection, but digital can approach it much more closely than analog.

112233 4y ago
Absolutely agree. Even more, once you are in digital, you can have actual mathematical perfection, that is reproducible and does not degrade with time. I just seem to take issue when Nyquist is getting inwoked. That is a purely mathematical result. It is sufficient (and I think required, too) to plug source into ADC+DAC, measure the output and show that the difference is insignificant. And much less than, say, with tape.