Can anybody help straighten me out on some SRC maths? Specifically, if I want to up-convert some files from 48K to 96K, then downconvert the mixed result, and if I have three sinc SRC converters, one with a BW limit of 80% (fast), one with 90% BW (medium) and one with 96% BW (best), then is it true that I could use any of the three to up-convert without losing anything (since 96K is 2x 48K, none of the three converters will actually lose any data on the way up)? Do I only really need to worry about losing fidelity on the way down?
I can answer that you can only loose fidelity on the way down or upsampling to a non 2X number since it’s not exactly twice the value so it wouldn’t be a smooth conversion, but this is almost all theoretical.
If you want to upsample 2X times up and then downsapmle 2X times back down, some people like “sound guru” Bob Katz say that this is perfectly fine and mostly needed for mastering since you will be adding twice the data of pure silence and when adding plugins which add more noise will be able to spread that noise making it lower (like same amount of water poured in a wider glass will be lower than in a tighter one), and because some plugins sound or do their math better with higher sample rates, and you would end up with a cleaner and better sounding file.
I say go for what you want, try it and hear it, don’t be lazy.
Unfortunately these type of questions get an array of non-proven answers, just theoretical.
The real answer tho the up or down sampling quality is what you think sounds good and what you think is right, that will make you more professional.
Just don’t do too many conversions…
SRC between any two rates, whether it’s up or down and whether they are in a simple ratio or not, is a complex digital filtering process and will introduce small amounts of noise in the same way that any processing (even just a gain change) will do.
I’m not clear why you want to convert up and then down…
@Michael Tiemann:
since 96K is 2x 48K, none of the three converters will actually lose any data on the way up
You give me the impression that you believe x2 conversions are better than x2.15367 conversions. That’s a myth invented by either ignorant audiophiles or wannabe-engineer GearSlutz types (who else?).
The mathemathical formula does not care if the output rate is 2x the input rate or 2.15367x or 3.14159x, the result will have exactly the same precision (or lack of) in any case.
up-convert without losing anything ... Do I only really need to worry about losing fidelity on the way down?
You lose the same if you go up or if you go down (if you use the same SRC). You lose in a technical sense, because in reality it’s inaudible even for the less refined (contemporary) SRCs, even for many passes. Ethan Winer did an experiment more or less about that in his part of the famous “Audio Myths Workshop” [ http://ethanwiner.com/aes/ ] where if I remember correctly (I can’t check the video right now) he played and recorded the music through a cheap consumer soundcard, and did so many times to see where the error became audible. I don’t remember what was the conclusion, but for many passes (more than you’d think) you couldn’t hear any difference. Note that both playing and recording through a souncard involves sample rate conversion internal to the soundcard’s chip, additional (although slightly different) to any your computer may be doing.
That doesn’t mean you shouldn’t try to use the best - you really should - but don’t let the issue make you sweat either, there are much more important things to worry about.
you can only loose fidelity on the way down or upsampling to a non 2X number since it's not exactly twice the value so it wouldn't be a smooth conversion
Eh, no.
since you will be adding twice the data of pure silence and when adding plugins which add more noise will be able to spread that noise making it lower
No. That’s misleading - “adding twice the data of pure silence” is part of the internal process of some SRC algorithms, but the other part of said process involves removing said silence.
About the noise: Firstly, well designed plugins don’t add noise, if you have a plugin that adds noise and it’s function is not to add noise, then your plugin is defective. Secondly, this noise would have nothing to do with quantization noise (a.k.a. dithering) - different noises, bro. Thirdly, any such noise even in the case of the defective plugin would be so low it would be inaudible. Lastly, “spread that noise” is misleading, upsampling doesn’t spread the existing quantization noise, it only adds more noise everywhere including the higher frequencies that are now allowed. Again, all this so low it’s not even remotely audible unless you’re working with 8bit audio.
some plugins sound or do their math better with higher sample rates
If your algorithm works better within the frequency range of the original sampling rate when you use a higher sampling rate, that’s a sure sign that your algorithm is wrong. If your algorithm has a valid mathemathical reason for working better with oversampling (for example a true peak limiter) then the necessary oversampling should happen within your plugin, as part of your algorithm, so that the result is always correct from the point of view of the original sampling rate. If you know of a plugin where this is not the case, go give it’s developer a good bash on the head. Tell him Xperienced sent you.
Unfortunately these type of questions get an array of non-proven answers, just theoretical.
Not if you can tune out the usual noise makers and concentrate on the one or two real experts that always jump in out of nowhere. 
The real answer tho the up or down sampling quality is what you think sounds good and what you think is right, that will make you more professional.
As an engineer it will make you less professional. Engineers don’t “think it sounds good” (that’d be wrong on many levels, I refer you again to the “Audio Myths Workshop” video for more information), engineers show you why it is good using scientific instruments and mathemathics. Of course this doesn’t apply when you have to make a decision about something fundamentally subjective, but sampling theory is not subjective in any way.
As a musician I think it is indeed the best thing you can do. You are supposed to hire (or be an) engineer to do those things, but I understand sometimes it’s not possible. Or limit yourself to using “For Musicians” products and trust the engineers who designed them. Either way, live and learn.
Just don't do too many conversions...
Where “too many” is probably a bigger number than you think. See above.
What, you thought you had escaped from my wrath? You silly, no one does that!
is a complex digital filtering process
Actually it’s a pretty simple digital filtering process. It’s hard to understand because it inherits the counterintuitiveness of the infamous Nyquist-Shannon theorem, but after it clicks in it’s very simple.
It annoys me when people call “complex” simple things (I see it often) because on one hand it discourages people who are perfectly capable of studying it from actually studying it and, on the other hand, it lends itself to creating more myths, which is the last thing this ~lovely~ industry needs.
I'm not clear why you want to convert up and then down...
Don’t quote me on it but I think the OP was only putting it to illustrate his question, not actually trying to do it.