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Re: Indeed.

OK,

I read this thesis:
Wannamaker, R.A.: "The Theory of Dithered Quantization", PhD-thesis, University of Waterloo, 2003

What struck me first is that a friend of mine is actually thanked in the acknowlegments (I had no idea, haven't talked to him in a while).

There is lots of interesting math but here are some interesting results:

Two types of dither: subractive (SD) and non-subtractive (NSD)

"First, the dither signal must be available for subtraction at playback in SD
systems, and so either the dither sequence or information suffcient to reconstruct
it must be stored or transmitted with the signal. On the other hand, SD systems can render the total error signal statistically
independent of the input signal as well as rendering error samples separated in time
statistically independent of one another."

Only SD dither renders the total error statistically uncorrelated with the input - the drawback is you need the dither signal used on encoding AND playback. So in essence you don't get something for nothing - your effective infinite resolution of your first signal requires passing on a second signal to the playback side.

"NSD systems, on the other hand, cannot render the total error statistically
independent of the input, but can only render specified moments of the error input
independent. Furthermore, dithers of successively higher order are required for
each moment to be so rendered."

NSD lets you not pass the dither to the playback side, but has the limitation that there is some correlation of the noise to the input.
This is the type of dither used in digital audio applications.

"In general, interchannel sharing of random numbers for the purposes of dither
generation will introduce interchannel correlations between error signals. This interchannel
error correlation may be undesirable in certain applications. For instance,
such correlations may affect the spatial image of the noise in multi-channel audio
signals."

The dither generators need to be careful about sharing noise signals across channels or channel error correlations would exist.

There is nothing discounting the idea that instanteous amplitude and phase errors still occur, but from the statistical standpoint the moments of these errors and statistically independent. Listening tests apparently show this to be good enough (although I did not see any mention of their listening tests comparing the actual analog signal + noise being tested against the different quantization levels - and certainly none mentioning multichannel).

I guess the question is what is the time contant the ear integrates over to determine how much we rely on statistics for perception (I would guess a fair bit). Obviously spectrum analyzers rely on statistics on windows of data, but the ear is a totally different animal - it is thousands of native frequency domain tranducers which are time modulated with amplitude information (rate of neuron firing repesents amplitude) and the fact that there are 2 of 'em gives relative phase info (and possibly as well the duty cycle of neuron firing?)

In another related paper fom his supervisors at Waterloo they spell out that DSD is inherently flawed (as are all 1 bit delta sigma schemes) since you cannot effectively apply dither to a 1 bit quantizer without saturating it which destroys exactly what dither is supposed to do! Yikes!


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