There is absolutely no technical, psychoacoustic or even preference reason why flat TPDF should sound better (or worse) than shaped dither.
Bob, I agree with that. Our ears are not flat and it makes perfect sense to steer the quantization noise from frequencies where we’ll notice to frequencies we’ll not notice.
And, again, PDF is not the same as spectrum. Looking at that dither schematic I posted, inside the loop it’s white TPDF dither just before the quantizer. But putting the loop around it then changes the frequency response from that white piece-wise quadratic pdf source (this is the dither + the actual quantization error, which is 4.77 dB more than just the quantization error by itself) to the output. And there’s a kinda cool theorem by Michael Gerzon and Peter Craven that shows that that curve that Alexey posted must have some area below the flat white noise and some area above it. That sorta says what the best we can do from an information theory perspective.
Brighter dither noise does not necessarily translate to brighter sound. Sometimes shaped dither makes the sound warmer and fuller. It’s all because of masking between elements of the source and the noise shaped dither.
In my opinion, I would expect well-shaped dither to just make it sound transparent. The 1644 should sound like the 2444. As much as possible. And, just to make sure, I would expect the quantization to be done at the final mastering sample rate. SRC should happen when the wordsize (or “bit depth” – which term should I use?) is larger. If it’s 24-bit fixed point, then all that SRC math can be done with higher precision words and finally written with good-dithered quantization at the final sample rate. But dithering the SRC output is not needed if the intermediate words were 64-bit floats. Then quantize to 16-bit, all at 44.1, with this MBIT+ thingie or the product of your delight.
I dunno shit about what you guys do in the trenches (and my hearing ain’t so good, especially being an old fart who listed to too much loud vinyl rock-n-roll in the 70s and whose dad had hearing aids), but mathematically it can only make sense to do the SRC with larger words and get it to 44.1 kHz before quantizing to 16-bit samples.