prof_peabody, your analogy leaves out something very important. Can I have a moment to explain it in a roundabout way? You are asking excellent questions but the method of visual imagery which you (and about a million other people) are trying to get answers from can't possibly do the trick.
Let me suggest that you consider the analog signals going into the digital recorder, the analog signals that come back out in playback, and a third analog signal: the output subtracted from the input--a/k/a the difference or change or error (a/k/a noise and distortion) caused by the recorder's imperfections.
We're trying to identify the inherent limitations of sampled representations of continuous waveforms, so let's make an "assumption for the sake of argument" that the converters in this recorder are as linear and quiet as they can ever be. We want to know which flaws are inherent to the process, and can't be overcome by better converters, better analog circuitry, better flashing lights or generally, by spending more money.
OK. To start with, of course one full cycle of a low-frequency waveform will be sampled more times than one cycle of a high-frequency waveform will be. But it's a mistake to conclude that the low-frequency waveform is getting a better description as a result. The conventional visual analogy breaks down completely on this point, and gives a wrong answer. What tells the truth is the analog "difference" or "error" signal that I mentioned earlier. In a well-implemented digital recorder, the magnitude of the "difference" or "error" signal will be about the same for the high-frequency waveform as it is for the low-frequency waveform.
That isn't a hypothetical statement. Almost everyone in this forum has the equipment and/or software to create "error" signals of this kind. They can be observed and measured by anyone, and indeed have been listened to and looked at and measured for decades. Doing so can be a big "oh!" moment for understanding digital recording. It's the real-world fact, and any mental models that we construct to help ourselves understand the process must take it into account.
So where does the "three data points vs. fifty data points" model go off the tracks? You might see something very interesting (but probably not hear it) if you could remove the anti-aliasing filters from your digital recorder. Nowadays they tend to be an integral part of the D/A converters, but in the early and mid 1980s when digital recording first entered the recording studios, they were physically separate components (though usually on the same circuit board). Those D/A converters really did deliver the stepped waveforms that many people imagine are at the output of a digital audio recorder; then the filters smoothed those waveforms out (though not just by simple linear interpolation as many people seem to imagine).
Still, you could insert a probe in between the two components and look at the D/A converter's direct output. And if you did that, and if you created an "error" or "difference" signal at that point, you'd see that the "difference" or "error" signal on high frequency inputs would have a different frequency spectrum from the corresponding error signal for low frequency inputs. Probably there would also be some difference in magnitude, just because nothing's perfect. But the main energy of both error signals would fall above the "one-half the sampling rate" frequency--and not incidentally, above the range of human hearing. So the anti-aliasing filter would leave you with smooth sine waves at both frequencies, if that's what you'd put in.
--best regards
P.S.: A closely related issue is low-level vs. high-level signals. A full-scale waveform is "described" with the full range of sample values--for a 16-bit system, all 16 bits are used, etc.--while a low-level waveform (say, at -60 dBFS) exercises far fewer bits. The "connect the dots" model predicts that the low-level signal will be less accurately represented, and will therefore have much greater distortion. Yet with any well implemented digital recorder this doesn't occur--a fact which it's not at all difficult to show nowadays.
Topic: Resample to 44.1 or record at 44.1 (midside Q) (Read 10067 times)