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Nope, this isn't right, Let me try to explain dither.

Howdy

Perhaps a different point of view might add some insight (assuming that this is different than JJ's deck which I haven't even glanced at.)

Dithering (when done properly) does add a little noise to the signal, but it also (statistically, hence the noise) reveals some of what's going on below the noise floor. It makes no assumption about what happens downstream, let alone assumptions about the DAC.

For example when disk seek rates and sizes were lower some digital audio editing systems worked in higher precision internally, but (unfortunately) only wrote, say 16/44.1 to the disc. Therefor each editing pass or session would loose significant info. By dithering just before writing at lower resolution they lost less info at the expense of some noise. No DACs involved...

A poor man's dither could be (ignoring signs etc., just to keep things simple):

add a random number between 0 and 1 least significant bit (of the result resolution) to each sample before chopping to the result resolution.

That's it. You're done, it works. For example: Use an input sine wave at an amplitude just below an lsb. With no dither you'd get all 0's in your output. With the dither algo above 10% of the time the sine wave's amplitude was 10% of an lsb you'd get an lsb, 20% ==> 20%, etc. You now have some information you didn't have before and it correlates to the real data (with some noise.)

There are technical reasons for choosing various distributions of random numbers, etc. but the process and results are similar.

In a hand waving sense SACD's DSD is similar and indeed after filtering can give back the original signal (with noise) and perhaps this is similar to what you are talking about, but it's still the case that dither doesn't require any particular DAC to work. Of course your selection of a DAC will affect the results of a dither signal, but it affects everything else too.

-Ted

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