Thanks for dumbing things down a little for me. My comment was mostly tongue in cheek. I think I have a decent grasp on things. I was lost when the math equations came up and I don’t think any amount of dumbing down the math will help, as I just don’t have the patience for it.
Cheers
I'm not sure if it's really dumbing it down, so much as it is trying to explain the philosophical purpose and implications of the theories underlying the tech. If anything, it's trying to synthesize a more general notion of the theory, which I would argue is more challenging than trying to understand the math. If I can't level the concept with everyone eye-to-eye and cannot effectively communicate its theory, I don't fully understand the concept. The math is more of a way of trying to objectify the theory and trying to manipulate it to understand its limitations, not the de-facto ground truth from which the theory happens to stem (a common mistake amongst engineers, and the very plague which drives physics and ironically enough drove me away from studying raw physics in college).
It is very nice video. Wforwumbo, I understand. It is good to think of the output analog signal as the original analog signal + frequency bandwidth limitation (due to sampling) + quantization noise (due quantization). And the imagine of stairs may be useful when we are modifying the digital signal in our DAW.
Sure, cheers. Just remember: it's an analogy for what's happening - not what's actually happening under the hood. Shoving samples around is more art than engineering (and in practice you don't actually shove the samples around, but that's outside the scope of this thread), it's a shame it's so much fun once you get it right because getting it wrong is like pulling your own teeth out.
That's a VERY high-level summary of what I've been trying to get at here for recording at 24/96 (or higher). At the end of the day, for playback you are totally fine listening to and distributing online 16/44.1 data. However, if you have an easily-accessible archive of 24/96 or 24/192, it allows post production people doing remixing work or mastering work a LOT more precision to do their magic, and the end result of the signal processed with filters at 24/192 that is then bounced down to 16/44.1 sounds significantly better (to my ear, at least) than info that was bounced down then processed at 16/44.1.
I am not sure whether or not you were being sarcastic, but this cracked me up! I am a taper, a hobbyist. My "post production people" are, well, me. I assume that is true for most of us here; it definitely is for the people I have discussed this with. I think, in general, tapers are pretty minimalist with respect to post-production. Many trim the ends and normalize and that's about it. Others (I am in this group) do some (typically light) EQ'ing, maybe some limiting for stray peaks, some noise removal, and normalization. A few go further, but, even in that group, we are often constrained by the limitations of the type of recording we do.
I would wager that for me (and probably many other tapers) the audible benefits of processing at 24/96 versus 24/28 are pretty marginal. In my case, I doubt it is worth doubling the file sizes. The standard rejoinder: "Storage these days is cheap!" Well, maybe, but I have a couple of drives in my tower and several more in my NAS. I upgrade (and add more) every couple of years and it is not inexpensive in my mind. On top of that, I have a cloud backup option that also costs quite a bit per year and will cost more as I increase the capacity.
I would be curious to hear your comments on rates greater than 96 kHz. Lavry, for example, says that there is a trade-off between speed and accuracy and that the optimal sampling frequency is around 60 kHz, with 88.2 or 96 being the closest typically available rates. [Also perhaps of interest to you is his way of describing the time/frequency relationship using sinc instead of Fourier functions.]
I came into taping as a studio guy - I have been doing studio production since high school, and the notion of applying my knowledge to my favorite tapers' work is how I got hooked. Eventually I got looped in by the raw sound of tapes and how to perfect that, since the studio adage goes that it's better to spend 20 times getting the right take and applying gentle (at most) filtering sounds infinitely better than spending hours trying to fix a subpar recording. I can say that I've learned LOADS from taping that has made me a much better studio engineer, but I'd like to flip that coin on its head and mention that lots of tapers could learn a thing or two from post production guys to make a better-sounding end product. Even if it's not for "cleaning up a recording," post production requires a careful ear that helps you tune your mic setup to optimize the amount of work you have to do after the fact, and the reason I started (and still continue) doing it is because that final layer of polish can be the difference between "yep this is great music" to "the veil of realism has been drawn, I can sit back and enjoy this recording without the tape getting between me and the music." I would counter-argue that the constraints from limitations of the recording is limited more by taper knowledge and experience toying with post production (followed by frustration of not putting in the time to learn how to equalize and do ear training), rather than a limitation of the medium or method of recording. Just like making a good tape, learning to apply effects in the post chain takes experience and lots of getting it wrong, before you learn how to get it right; and lots of studio guys would stick their noses in the air at how/why we do things, without understanding how it would make their lives way easier.
The difference isn't marginal - it's pretty significant. I really DO need to get sound clips up here, as it'll prove my point better than words. And likewise, it's something I encourage you to try out on your own next time you make a tape, or grab some 24/96 tapes that are uploaded (most of my tapes are up on eTree as 24/96, happy to get you a copy if the torrents are dead). Play with it yourself by doing the filtering at 24/96 and bouncing down to 16/44.1 after processing, versus doing the identical processing at 16/44.1, and see if you really can or can't hear a difference. That does more talking than any amount of typing I can do behind a screen.
I've taped and tracked at 24/192 before, personally it's past the practical limit given wav files can only contain 4 gigs, and given I run 4-6 channels it's just too much bouncing individual tracks/merging them to create sets. 24/96 I can usually squeeze a set of music running 4 channels without needing to splice. The benefits between tracking at 96 and 192 are there to my ear - I've picked them out when double-blinded - but the filter error is low enough to me at 24/96 that I care a little less about the bump up to 192. If there were tech to make my life easier to track and splice/join stereo pairs of tracks at 24/192, I'd do it in a heartbeat and without batting an eye.
I don't think there's a real "optimal" speed/accuracy tradeoff curve for sampling. There are just too many ways to process audio for there to be a magical number for it to boil down to. You can halve your buffer size if you double the sample rate, and have the same effective latency as the same number of samples-per-unit-time are being processed. Seeking an optimal rate is imo a bit of a fallacy - just go as fast as you can accurately and conveniently sample once you are past Nyquist, which is the point of my posting here. If that's 24/48, so be it.
Curious what you mean about using sinc instead of Fourier "functions" - the Fourier transform listed on the last page is a synthesis function that decomposes a signal into a summation of cosine and sine waves that exist within the time signal. The sinc function [a sine divided by the index of the sine, so sinc(x) = sin(x) / x] pops up a whole bunch in filter design engineering with good reason, but I've never seen it used as a domain transform variable.