utility seems to depend on the channel through which the signal needs to be transmitted. for wireless telecom, there is a lot of bandwidth with extra side bands that carry auxiliary data. ideally, you wouldn't even need to mathematically re-derive the added 'subtractive' dither signal to recover the noise floor if you can just transmit the pure dither signal along with your signal, and just decode and subtract
On Sat, Nov 20, 2021 at 10:56 PM robert bristow-johnson < r...@audioimagination.com> wrote: > 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 which 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------ > *Fro m: *Sampo Syreeni > *Date: *Sat, Nov 20, 2021 6:59 PM > *To: *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 <+de...@iki.fi>, > http://decoy.iki.fi/front+358-40-3751464, 025E D175 ABE5 027C 9494 EEB0 E090 > 8BA9 0509 85C2 > >
