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[Chris Caudle]

On Thu, February 28, 2019 4:17 am, Anahata wrote:
> I usually choose "triangular", for what it's worth.

Triangular, either shaped or flat, is the appropriate distribution
function to use.

No dither will cause the quantization noise to be highly signal
correlated, i.e. what most people would call pure distortion rather than
noise.  No dither is never the appropriate choice.

Rectangular probability distribution function will still cause some
correlation of the quantization noise with the signal, so the quantization
noise sounds like what you would call noise rather than distortion, but
the noise is not constant, it can
"pump" with the signal level.   I do not know why rectangular PDF is even
a choice, it saves a trivial amount of processing power and is
mathematically shown to not serve the purpose of making quantization noise
fully independent of the signal.

Triangular probability distribution function has been shown mathematically
and through listening tests to make the quantization noise audibly
independent of the signal, which is the desirable situation.

Shaped noise is just an equalized version of the dither signal (assuming
it is really just shaped dither, and not a scheme with a feedback loop). 
Same noise modulation requirements apply, if the dither is going to be
shaped it should still start as triangular PDF, but will have to be higher
amplitude overall to account for the energy removed by the filtering. 
Usually provides no audible benefit in my experience, although the benefit
is at least arguable, unlike the choice of no dither or rectangular PDF
which are mathematically demonstrably wrong.

I don't want to come across as rude, but please ignore completely what
Gunter wrote, it was essentially wrong in every point.  If you really want
to understand the mathematical basis behind quantization then please
search out papers by Lipshitz and Vanderkooy, or the PhD thesis of their
student Robert Wannamaker, "The Theory of Dithered Quantization."
Can be found online here:
http://www.robertwannamaker.com/writings/rw_phd.pdf

If you don't care to understand the details then just pick triangular
dither and get on with making music.

-- 
Chris Caudle