On 2021-11-20, Ethan Duni wrote:
If I follow correctly the intended application is space communications, where bandwidth/power is at a premium.
Can be, but I started out with just audio.
The thing about subtractive dither is that any processing on the digital signal will disturb it.
The point is to subtract it before any processing, and then to add it in after. What you have then is the cleanest signal to processs while processing, and the best transfer signal before and after. Statistically speaking.
Additive dither with noise shaping is already pretty good on 16+ bit converters, so for most modern audio applications it’s hard to justify.
...and the point is that you can do both subtractive and additive at the same time. If you do just additive rectangular probability distribution function (RPDF) dither of one least significant bit peak-to-peak, you will decouple the first moment of the error function in discretization. That will lead to noise modulation at low amplitudes. If you do triangular probability density function white noise (TPDF), so that you sum two independent sources of RPDF together as the dither signal, you'll decouple the error to the second degree. But not the third.
Try it out yourself, because it's easy to hear: put a 1kHz constant test signal out at sqrt(2) scale, and sum it with a sqrt(2) amplitude semi-fast linear sweep tone. Even at 14-16-bit resolution, you will hear a third order intermodulation product when using additive dither. When using subtractive dither, you will hear none. Just the lowest noise floor that is theoretically possible.
And that noise floor won't compound after multiple processing steps, as it does with additive dithering. It *will* compound at the minimum floor, of course. But that floor is a whole 6dB lower for subtractive dither, as opposed to additive RPDF, and evenmore for the typical TPDF additive signal.
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