Logic Pro 9 dither chain

Question

Where in the master fader chain does Logic Pro 9 convert 24-bit recordings to 16-bit files and apply dither (if chosen in the bounce to disk dialog)?
Is it post master fader, pre master fader...?
If I use a Waves L3-16 multiband limiter as the last plugin on Logic's master fader channelstrip and I choose to use it to convert 24-bit recordings to 16-bit files, where in the master fader chain does that happen, post master fader, pre master fader...?
In Digital Performer there is a way to make a plugin slot post fader, and when mastering, you are supposed to convert to 16-bit files and apply dither post master fader with the master fader at 0.
Thanks for any insight on dithering and convert to 16-bit files in Logic.
======
Richard

Answer 1

Bee Jay wrote:
What you are doing, is that a 32-bit float number stream goes into the L2, and a 32-bit float number comes back out of the L2, except now that 32-bit float number stream contains a much smaller 16-bit dithered numbers - in effect, you're still in 32-bit float, but you've just thrown away a huge amount of resolution, which is better preserved right until the end and used to make a better output conversion.
A good time to clarify the distinction between dithering and truncating. Applying 16-bit dither does not throw away any resolution. Typically, the immediate next step is truncation, which does throw away the data. In a textbook case of dithering, the steps would be 32-bit float -> 24-bit fixed -> apply 16-bit dither (data still contains 24-bits of resolution)-> truncate to 16-bits.
I'm not sure whether that resolution is being thrown away from the "top" or the "bottom" of the number range. I'm not sure how that works, maths/DSP wise.
With 32 bit FP audio, 8 of those bits are used for the exponent, leaving roughly the same resolution as a 24-bit fixed representation when comparing the accuracy of quantized amplitude.
In short, it seems to me that trying to downconvert in the middle of a 32-bit float stream is a not terribly great thing to do, for the reasons outlined.
I agree. But applying 16-bit dither in the middle of a 32-bit float stream isn't necessarily the same thing. The important question is whether or not the ultimate 16-bit fixed output will be altered downstream from the dither. My assumption is that as long as faders are left at unity and no processing is done, the 16-bit output at the end will be unchanged. But I may be wrong...
Here's the thing, though... if you're correct, Bee Jay, and those resulting 16-bits get altered post-dither (even with no deliberate processing or fader manipulation), then you're essentially saying that it's impossible to apply 16-bit dither properly in a 32-bit floating environment. Since all the major native plug-in environments are 32-bit float (AU, RTAS, VST), we'd then have to conclude that all of those native dithering implementations by Waves, iZotope, etc., are worthless, eh ? That seems unlikely, but again, maybe there's someone on this forum who can confirm 100% one way or the other...
-James