Chris Hornbeck wrote:
On Fri, 21 Nov 2003 20:40:02 GMT, Jim Gilliland
wrote:

OK, now _I'm_ the one who's confused. I thought that what Ulysses wrote
above was pretty well established and non-controversial, and furthermore
that you (Chris) were already in agreement with it (based upon your post
back to me just a few minutes earlier). So what exactly is
contradictory here? What does Watkinson say that seems to counter the
above?

Watkinson's The Art of Digital Video, 2nd ed. pg. 143-144 (sorry,
don't have The Art of Digital Audio handy):
" the principles of analog and digital dither are identical; the
processes simply take place in different domains using two's
complement numbers which are rounded or voltages which are quantized
as appropriate. In fact quantization of an analog dithered
waveform is identical to the hypothetical case of rounding after
bipolar digital dither where the number of bits to be removed is
infinite, and remains identical for practical purposes when as few
as 8 bits are to be removed. Analog dither may actually be generated
from bipolar digital dither (which is no more than random numbers
with certain properties) using a DAC."

Hopefully, I'll be shown to have misunderstood the above, and can
go back to my comfortable but fuzzy understanding of things before
this blasted thread started. Ignorance was bliss, and I'm too old
to study.

OK, all of your quote makes sense to me. What I don't see, though, is
how anything in Ulysses's quote contradicts it. Here is what you quoted
from Ulysses earlier - can you help me see where the conflict is? I
apologize if I'm being dense or stupid here.

I know Mithat, and he knows what he's talking about. If he didn't, he
wouldn't have written it. He's not saying that dither can't be applied
in the digital domain. He's saying it needs to be applied prior to the
quantization (or re-quantization) that's being dithered.
In an ADC, this could occur in the analog domain, or in the case of an
oversampling converter, it could be done digitally before the signal is
quantized to 16 or however many bits.

In the case of truncating 24 bit data into 16 bits, he's saying you
have to add the dither BEFORE you lop off those bottom 8 bits. The
dither and the LSBs have to be summed before truncation.