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Dithering for

Started by Yazz December 1, 2006
Hopefully some of you guru's here can set me straight here.

In an attempt to reduce quantization spurs, I have read about
dithering.  I have seen wideband dithering and narrowband dithering.
All of this is done in the analog domain prior to the sampling.

My question is:  Why can we not simply add a random LSB (+/- 1) to each
of the samples AFTER sampling to reduce quantization spurs ?


Seem like this would help uncorrelate the error signal from the
quantized signal.

What happened when you simulated it?

Dirk

Yazz wrote:
> Hopefully some of you guru's here can set me straight here. > > In an attempt to reduce quantization spurs, I have read about > dithering. I have seen wideband dithering and narrowband dithering. > All of this is done in the analog domain prior to the sampling. > > My question is: Why can we not simply add a random LSB (+/- 1) to each > of the samples AFTER sampling to reduce quantization spurs ? > > > Seem like this would help uncorrelate the error signal from the > quantized signal.

Yazz wrote:

> Hopefully some of you guru's here can set me straight here. > > In an attempt to reduce quantization spurs, I have read about > dithering. I have seen wideband dithering and narrowband dithering. > All of this is done in the analog domain prior to the sampling. > > My question is: Why can we not simply add a random LSB (+/- 1) to each > of the samples AFTER sampling to reduce quantization spurs ? > > > Seem like this would help uncorrelate the error signal from the > quantized signal. >
This is nonsense. Read the chapter about dithering again and try to understand it. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
"Yazz" <yazz35@gmail.com> writes:

> Hopefully some of you guru's here can set me straight here. > > In an attempt to reduce quantization spurs, I have read about > dithering. I have seen wideband dithering and narrowband dithering. > All of this is done in the analog domain prior to the sampling. > > My question is: Why can we not simply add a random LSB (+/- 1) to each > of the samples AFTER sampling to reduce quantization spurs ? > > Seem like this would help uncorrelate the error signal from the > quantized signal.
Here's a thought experiment that shows it cannot be done this way. Assume you have an analog DC input signal that is exactly one-fourth of the way between one quantization level, say, n*q, and the next, (n+1)*q. Without dithering, the A/D input becomes a constant n*q. The information that the input level actually resides at 1.25*n*q is lost. Adding noise ("dither") to n*q just gives you a noisier n*q, not a noisy 1.25*n*q. -- % Randy Yates % "Midnight, on the water... %% Fuquay-Varina, NC % I saw... the ocean's daughter." %%% 919-577-9882 % 'Can't Get It Out Of My Head' %%%% <yates@ieee.org> % *El Dorado*, Electric Light Orchestra http://home.earthlink.net/~yatescr
Randy Yates <yates@ieee.org> writes:

> Assume you have an analog DC input signal that is exactly one-fourth > of the way between one quantization level, say, n*q, and the next, > (n+1)*q. Without dithering, the A/D input becomes a constant n*q. > The information that the input level actually resides at 1.25*n*q > is lost. Adding noise ("dither") to n*q just gives you a noisier > n*q, not a noisy 1.25*n*q.
These "1.25*n*q"'s should be (n+0.25)*q instead, but I hope you still get the point. -- % Randy Yates % "My Shangri-la has gone away, fading like %% Fuquay-Varina, NC % the Beatles on 'Hey Jude'" %%% 919-577-9882 % %%%% <yates@ieee.org> % 'Shangri-La', *A New World Record*, ELO http://home.earthlink.net/~yatescr
Randy Yates wrote:
><snipped> > Here's a thought experiment that shows it cannot be done this way. > > Assume you have an analog DC input signal that is exactly one-fourth > of the way between one quantization level, say, n*q, and the next, > (n+1)*q. Without dithering, the A/D input becomes a constant n*q. > The information that the input level actually resides at 1.25*n*q
Shouldn't that be (n+.25)*q, not 1.25*n*q ?
> is lost. Adding noise ("dither") to n*q just gives you a noisier > n*q, not a noisy 1.25*n*q. > -- > % Randy Yates % "Midnight, on the water... > %% Fuquay-Varina, NC % I saw... the ocean's daughter." > %%% 919-577-9882 % 'Can't Get It Out Of My Head' > %%%% <yates@ieee.org> % *El Dorado*, Electric Light Orchestra > http://home.earthlink.net/~yatescr
Yazz wrote:
> Hopefully some of you guru's here can set me straight here. > > In an attempt to reduce quantization spurs, I have read about > dithering. I have seen wideband dithering and narrowband dithering. > All of this is done in the analog domain prior to the sampling. > > My question is: Why can we not simply add a random LSB (+/- 1) to each > of the samples AFTER sampling to reduce quantization spurs ?
You can not regain information once you've thrown it away. If you add dither after rounding or truncating (which throws away any fractional information), then you just add noise. If you dither before rounding or truncation, then you spread out the fractional information (a +0.25 fraction could become from -n.75 to +n.25) into a probability distribution where the fractional information might be able to leak thru the quantization process, given a statistically large enough number of samples. The randomization of the dither noise actually prevents the information from being completely thrown away, but, in exchange, hides it in noise. In both cases you get noise, but in the pre-dither case, you get more information about the signal hidden in the noise. A patterned dither, or fraction saving process, instead of a random dither, allows one to deduce even more information about the signal as it was prior to rounding or truncation, by making some of the noise more removable. IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M
Ron N. wrote:
> Yazz wrote: >> Hopefully some of you guru's here can set me straight here. >> >> In an attempt to reduce quantization spurs, I have read about >> dithering. I have seen wideband dithering and narrowband dithering. >> All of this is done in the analog domain prior to the sampling. >> >> My question is: Why can we not simply add a random LSB (+/- 1) to each >> of the samples AFTER sampling to reduce quantization spurs ? > > You can not regain information once you've thrown it away. > > If you add dither after rounding or truncating (which throws > away any fractional information), then you just add noise. > > If you dither before rounding or truncation, then you spread > out the fractional information (a +0.25 fraction could become > from -n.75 to +n.25) into a probability distribution where > the fractional information might be able to leak thru the > quantization process, given a statistically large enough number > of samples. The randomization of the dither noise actually > prevents the information from being completely thrown away, > but, in exchange, hides it in noise. > > In both cases you get noise, but in the pre-dither case, you > get more information about the signal hidden in the noise. > A patterned dither, or fraction saving process, instead of > a random dither, allows one to deduce even more information > about the signal as it was prior to rounding or truncation, > by making some of the noise more removable. > > > > IMHO. YMMV.
An interesting and instructive answer from the information / statistics point of view. Another way of looking at the question is to examine what happens when a repetitive, constant-amplitude test signal is applied. If its frequency is a simple fraction of the sample frequency, the quantisation noise is also repetitive, and repeats over a few cycles of the test signal. In the frequency domain the effect is that 'spurs' appear, and these are harmonically related to the test signal. If dithering is now applied to the test signal it disrupts the regular nature of the quantisation noise, spreading out the spurs in the frequency domain. This brings me to my main point. Is dithering have any other use apart from improving the test-signal results? It seems to me that dithering does not provide any benefit at all when 'real-life' audio or video signals are being sampled, and I would be interested if anyone disagrees with this. My argument is that real-life signals are neither constant-amplitude nor constant-frequency nor repetitive. This should mean that the quantisation noise will not be repetitive either. As a result, any 'spurs' which occur will be highly transient and are will not be perceived as tones in audio signals or patterns in video signals. In effect, when real-life signals are sampled, the non-repetitive nature of signals should suppress the production of spurs in exactly the same way that dithering suppresses spurs when test signals are sampled. Regards, John
John Monro wrote:

   ...

> This brings me to my main point. Is dithering have any other use apart > from improving the test-signal results? It seems to me that dithering > does not provide any benefit at all when 'real-life' audio or video > signals are being sampled, and I would be interested if anyone disagrees > with this. > > My argument is that real-life signals are neither constant-amplitude nor > constant-frequency nor repetitive. This should mean that the > quantisation noise will not be repetitive either. As a result, any > 'spurs' which occur will be highly transient and are will not be > perceived as tones in audio signals or patterns in video signals. In > effect, when real-life signals are sampled, the non-repetitive nature of > signals should suppress the production of spurs in exactly the same way > that dithering suppresses spurs when test signals are sampled.
Consider a signal (it might as well be repetitive) with a peak-to-peak amplitude of 1 LSB. (The question of this signal's shape is without meaning.) This signal is undetectable in the absence of noise and dither, but with appropriate dither or fortuitous noise, An FT will show it clearly. Is that counterexample enough? Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
John Monro wrote:
> This brings me to my main point. Is dithering have any other use apart > from improving the test-signal results? It seems to me that dithering > does not provide any benefit at all when 'real-life' audio or video > signals are being sampled, and I would be interested if anyone disagrees > with this.
> My argument is that real-life signals are neither constant-amplitude nor > constant-frequency nor repetitive. This should mean that the > quantisation noise will not be repetitive either. As a result, any > 'spurs' which occur will be highly transient and are will not be > perceived as tones in audio signals or patterns in video signals. In > effect, when real-life signals are sampled, the non-repetitive nature of > signals should suppress the production of spurs in exactly the same way > that dithering suppresses spurs when test signals are sampled.
I think most serious signal processing people would massively disagree with the notion than dithering only improves artificial things, and it isn't just about audio or video. Sure, dithering gets oversold in a lot of cases. Processing what is essentially a single shot event isn't going to be improved by dithering. Most signals are, however, somewhere between single shot and totally repetitive. The more repetitive they are, the more they gain from dithering. Many real world signals are extremely repetitive. I have greatly improved performance in energy metering through dithering. Power waveforms change rather slowly in the real world, and you get almost 100% of the possible benefit dithering could give. Regards, Steve