kryptonaut wrote:Thanks for posting your thoughts on digital sampling - it's always good to try to clarify these things, and an alternative perspective on a technical matter can be a big help in creating a more intuitive understanding.
However, if I can make a couple of (hopefully constructive) comments on your articles:
Firstly, I think there is possible confusion when talking about an 'audio sample' or a 'digital sample', as these terms are frequently used to mean a digital representation of a whole sound, rather than an individual value at a fixed point in time. It might be worth finding some terminology to avoid this potential confusion, especially if you are aiming your article at the novice. I think point 3 on your third post uses 'sample' to mean essentially 'digitised clip' whereas points 1 and 2 use 'sample' to mean an individual digital value.
Secondly - and you might disagree here - I think it's much clearer to think of a digital sample as simply a measurement of the analog signal at an instant in time, conveying no information about what values the analog signal took between this and the next or previous measurement. After all, that's what the word 'sample' means. Of course, by ensuring the analog signal had certain bandlimited properties before sampling, it is theoretically possible to reconstruct it accurately from these instantaneous measurements (together with the knowledge of the bandlimited properties) - and this reconstruction may involve generating an analog approximation to a scaled impulse from each digital sample, but I don't think it's really accurate to say that a digital sample is a scaled impulse any more than an array of numbers is a sound. So in your first post, where you say "conversion to discrete time adds high frequency components not in the original signal," I think it would be more correct to say "conversion from discrete time to an impulse stream adds high frequency components not in the original signal," and these components must subsequently be filtered out to reconstruct the analog signal.
I hope that makes some kind of sense - I think it's a great idea to cast some light on a theory that can sometimes seem a bit arcane, but I also think it's essential to avoid causing further confusion by using possibly ambiguous terminology.
Good points, don't disagree, but to elaborate:
Point #1: My #1 states "individual digital samples", so no ambiguity there. For point #2, I think it's clear that following #1 that when I say there are zeros between the samples, I mean each and not just confined to being between some individual samples and not others. If not, it becomes clearer later on (these are bullet points, after all). Yes, #3 (parsing, "...samples...don't represent...audio") necessarily refers to a group samples and not arbitrary individual ones. That's certainly the one that requires some unstated understanding of the concepts involved. But again, it's a bullet point, where brevity is key. Bullet points rarely explain everything you need to know—they are are there to be sticky for your brain. Anyway, agree completely on your point, just thinking it through here, and probably won't change it.
One your point #2, I do agree. It's more intuitive to explain capturing regular momentary levels—like motion under a strobe light, video frames, etc. But...The problem is that it's not convenient to move forward mathematically from there.
As I noted, I would rewrite the video script from scratch each time I would get back to it (a few months in between, it made more sense to start over that to wedge/mod other ideas into the previous draft). On most (all?) of these I started out with an explanation of taking measurement of regular points in time. But I want to get to the modulation in PCM, so I need to explain how it's equivalent to...This time I decided to skip that and go right to "sampling is equivalent to this...". The biggest change in the final draft (er, of the article, which is the first draft of the video) is that I added the history of analog sampling. Part of the logic there is I wanted to get the point across that "digital" is just a convenience. The magic is in the PAM, in the analog domain. PAM is very easy to explain mathematically, you need only accept how amplitude modulation works (the video will so a lot better here—I made the executive decision that I didn't have time to make a really nice AM-lab widget for the article). Veteran synthesists and various types of engineers will have an advantage there, certainly.