Okay this is hard to punch in on my phone.The *only* operational difference between additive and subtractive dither is that the latter has the *possibilty* of subtracting the added dither leaving only the uncorrelated (to the 2nd moment) quantization noise. To regain that 4.77 dB lost when adding TPDF dither to the signal immediately before quantizing to a shorter word length.The net kernal of this Gerzon insight is that you can use the LSB bit of the previous 128 samples, put those 128 noisy bits into a big messy logic mess to scramble them bits up even more. From those scrambled bits, two uniform p.d f. pseudo-random words are derived that are added to become the TPDF dither word that is added to the longer wordlength signal immediately before quantization. Adding that adds 4.77 dB to the noise floor.At the receiver end, that triangular p.d.f. dither word can be rederived from the same 128 LSBs of the quantized data sent over the stream and subtracted from quantized signal wh ich should recover that 4.77 dB of lost noise floor.Even if there is noise-shaping in the quantization, this dither can be identically filtered and subtracted at the receiving end and i would expect some theoretical gain, if not the 4.77 dB.Otherwise, don't subtract. You're no worse off with the additive dither than you would be otherwise. The dither generated this way is still useful dither.Powered by Cricket Wireless------ Original message------From: Sampo SyreeniDate: Sat, Nov 20, 2021 6:59 PMTo: MUSIC-DSP@LISTS.COLUMBIA.EDU;Cc: Subject:Re: about subtractive dither, for audio and other use (also scientific)On 2021-11-20, Zhiguang Zhang wrote:
> from what i've been taught, the function of dither is to decorrelate > noise from the signal. This is what I'm aiming at. But there are two different types of dither: subtractive and additive. Additive dither is what we now use, because it works well enough for audio work: when you add one bit's worth of RPDF dither before your ADC, you decorrelate the mean of the signal from the error signal. When you add another independent RPDF's worth, leading to a TPDF signal, you decorrelate/decouple the second statistical momentum, or in the audio circles, power/RMS amplitude. Thus, noise modulation no longer happens with TPDF. If you want to proceed with the exercise, you can: adding a third independent RPDF to the mix, will decouple to the third order, so that skewness is now decoupled. If you add the fourth, kurtosis decouples. And so on. Eventually you will arrive at a Gaussian distribution, which decouples all of the statistical momenta. The trouble with additive dither though, is that in order to get to the asymptotic statistical extrememum, you really have to add more and more noise of invariant peak-to-peak amplitude of 1 least-significant bit. So the noise piles up. You cannot just reason with it being of certain shape in the statistical distribution sense, but it has to be 1-bit RPDF, one over another, momenta per momenta, in order to do its job. At the same time, if you can do subtractive dither, it decouples all of the momenta at the same time. Plus, you can just subtract it out, as per the name of the algorithm. If you send out a subtractively dithered signal, then receive it, then recode it, and then redecode it, pretty much no extra noise has been gained in the process. A digital channel which has been subtractively dithered like this, over and over, basically works as if it was an analogue, lossless wire: with regard to the noise floor set by the bitwidth, it's almost fully transparent, so that a network of such connections from place to place, functions more or less as an idealized analogue circuit, with a well defined noise floor. As you can imagine, this sort of thing would make many difficult things easy, and many impossible things only hard. ;) > so it seems what you're suggesting is using signal statistics to > generate an optimum dither for signal enhancement? No enhancement. Just a self-synchronizing trigger for subtractive dither. So that I could come up with high grade and easy to implement subtractive dither, for general PCM circuits. -- Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front +358-40-3751464, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
