Dithering for

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.
�����������������������������������������������������������������������

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