Sound travels (if I mathed it correctly) 0.343mm in a microsecond.
I don't think I could detect any sonic differences attributable to that level of precision.
There are a few 5-ish microsecond reports. This does seem extraordinary, but this number continues to show up. Such resolution must be on very, very specific, perceptually enabled kinds of signals, of course. One person has claimed 2 microseconds, but there are some confounding issues, and I doubt that is relevant.
Interestingly, the 5 microsecond number is almost exactly 30dB down the first attack on the wider cochlear filters. 30dB is the SNR of the inner hair cells. So there is even an arguable (BUT UNPROVEN!!!!) mechanism that could provide this, again, for very specialized signals. VERY specialized. And nothing any human wants to hear, too, seriously. Think short 10kHz modulated pulses for one example. A proper response to that is "ow!".
By the way, sine waves modulated by a gaussian pulse are also a great way to prove that sub-sample time resolution in a PCM system very obviously exists. You just shift the time a tiny bit, and there you are, purely in band (to 120dB or whatever you choose) signals moved a tiny fraction of a sample.
Of course, if very, very subsample resolution did not exist in PCM, modems, disc drives, orthonormal filter banks, etc, would all not work. As we all know, by using a cell phone and a computer, they do work.
If the original signal is not band limited, reconstruction is underdetermined and there are infinite number of solutions to he reconstruction problem. Now the question is which one of those infinite number of waveforms do you choose? And therefore JJ's question of what is the original? How do you define accuracy, i.e. what is a more "accurate" reconstruction when you have to guess the missing information?
Exactly. As the deck I pointed to in #25 that somebody apparently vaguely objects to (and who will not provide specifics) exactly what you will see as "error" in a time-domain signal that is downsampled without filtering is precisely predictable, and will show up in the passband (0-FS/2) of the new lower sampling rate. These will be frequencies not in the original passband, and will sound anywhere from kind of bad to intolerable headphone-throwing bad. And that is easily measured by simply comparing the in-band spectrum (at the lower sampling rate) to the original signal in that bandwidth.
For upsampling, images (frequency images here, not pictures) rather than aliases will occur, adding energy that wasn't in the original signal, and NOT adding any that was present in the original signal at the higher frequency (that information is gone forever). Often these are out of the pass band, and may not be audible, but will give your tweeter and other equipment literal heartburn.
SACD has similar problems, but with noise instead of images, if you don't filter it above 50kHz quite sharply to remove the high frequency noise. The noise arises from completely different sources, however.
But even with the somewhat faulty explanation involving only tones, it makes the point clearly enough.
