John Monro wrote:
> 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.

In real life, the ears and eyes of mammals use a process very
much like dithering to improve sensitivity of certain kinds of
inputs. (Eyeballs, unlike cameras with very slow film, don't work
very well when clamped and aimed at still target images).


IMHO. YMMV.
-- 
rhn A.T nicholson d.0.t C-o-M

Vladimir Vassilevsky wrote:
> 
> 
> John Monro wrote:
> 
>> With music like that, who cares if there are a few 
>> harmonically-related spurs present?  They may be an improvement!   :=)
> 
> The problem is the spurs are not just the harmonics, but all kinds of 
> intermods between the sample rate and the input frequency.
> 
> VLV

Vladimir,

Thanks for that.  This thread is helping me clarify my thoughts on the 
subject.

Regards,
John

Jerry Avins wrote:
> John Monro wrote:
> 
>   ...
> 
>> Apart from this I would expect the decimation to yield one extra bit 
>> of resolution and 3dB improvement in S/N ratio for every factor of 2 
>> that the sample rate is reduced.
> 
> Square root of number of samples. 3 dB is half a bit.
> 
> Jerry

Jerry,

Thanks for the correction.  It should be 1/2 bit resolution improvement.


Regards,
John

John Monro wrote:

> The question is: in your counterexample, would dithering lead to
> a perceived improvement to the quality of the audio signal ?

Dithering is an application of stochastic resonance which also occurs 
in the ear with beneficial effects. There was an article in 
Scientific American about that:

F. Moss and K. Wiesenfeld, "The benefits of background noise", 
Scientific American 273, 66-69 (1995)


Martin

-- 
Quidquid latine scriptum sit, altum viditur.

John Monro wrote:

   ...

> Apart from this I would expect the decimation to yield one extra bit of 
> resolution and 3dB improvement in S/N ratio for every factor of 2 that 
> the sample rate is reduced.

Square root of number of samples. 3 dB is half a bit.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

John Monro wrote:
> Jerry Avins wrote:
>> Jerry Avins wrote:
>>
>>   ...
>>
>>> Noise would not be an improvement. Under conditions where external 
>>> noise sources don't mask it, the detected 1/5-bit signal can be 
>>> clearly audible with an evident pitch.
>>
> Interesting!  I would not have expected that.
> 
>> 1/5 --> 1/2. As a signal fades to silence, the quantizing becomes 
>> evident, and sometimes that is intrusive. Dithering makes it less 
>> intrusive. Perhaps because the low-level noise tends to mask some of 
>> the artifacts, but also because it suppressed them. If you want to 
>> explore the effects of dithering, quantize your audio to five bits or 
>> so, with and without dither, and with different depths of dither. I 
>> haven't done that myself, but I've heard the results and I'm a 
>> believer. It's much harder to hear a good signal made slightly better 
>> than it is to hear a bad one edge toward passable.
>>
>> Jerry
> 
> Was speech or music being used, rather than a test tone?

Both speech and music. 4-bit speech is intelligible if the speaker (or 
electronics) limits the dynamic range.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

John Monro wrote:

> With music 
> like that, who cares if there are a few harmonically-related spurs 
> present?  They may be an improvement!   :=)

The problem is the spurs are not just the harmonics, but all kinds of 
intermods between the sample rate and the input frequency.

VLV

dbell wrote:
> John,
> 
> Suppose you decide to increase the sample rate to much higher than the
> signal BW, add wideband dither noise prior to sampling, wideband in
> relation to the high sample rate, sample with very coarse resolution,
> then digitally decimate the signal, removing most of the quantization
> noise in the process. Would you expect the quality to go up?
> 
> Dirk
> 
Dirk,
This thread has been educational to me and has clarified a few things. 
Randy in particular pointed out that dithering is helpful in reducing 
the grainy effect for signals down near the bottom of the range of a CD, 
so to answer your question I would say that the dithering in your 
example could improve the quality by removing granularity in those cases 
where the audio signal frequency happened to be a near-exact fraction of 
the sample rate.

Apart from this I would expect the decimation to yield one extra bit of 
resolution and 3dB improvement in S/N ratio for every factor of 2 that 
the sample rate is reduced. This improvement would occur regardless of 
whether the dithering is turned on or off.

Regards,
John





> 
> John Monro wrote:
> 
> <snipped>
> 
>> Thanks for the counterexample Jerry. Dithering clearly makes the signal
>> detectable, and this has advantages for measurement where multi-sample
>> averaging is carried out.  You and Steve refer to this in later postings.
>>
>> The question is: in your counterexample, would dithering lead to a
>> perceived improvement to the quality of the audio signal ?  I can't see
>> that it would, because the 0.5-bit amplitude signal which was previously
>> undetected in the absence of dithering now gets sampled as a 1-bit noise
>> signal.  This is hardly an improvement!
>>
>> Regards,
>> John
> 

Steve Underwood wrote:
> John Monro wrote:
>> Steve Underwood wrote:
>>
>>> 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
>>>
>> Thanks Steve.
>> I take your point about measuring highly repetitive signals.  I was 
>> not thinking about this situation, which has some of the 
>> characteristics of the 'test-signal' I mentioned but is if course a 
>> real-life application.  I was thinking more in terms of audio or video 
>> signals, and in the perceived quality of the sound or picture.
>>
>> To re-state the question, does anyone disagree with the following 
>> statement?
>> "For 'real-life' audio or video signals, adding dithering to the 
>> sampling process does not make any perceptible improvement to the 
>> quality."
>>
>> I think it is true, and while I can present a theoretical argument, I 
>> don't have the equipment or environment to check whether it is true.
>>
>> Regards,
>> John
> 
> Signals are not one shot or totally repetitive. They are on a sliding 
> scale. For most of its duration, each millisecond of music has a lot of 
> similarity with the millisecond before and the millisecond after. It is, 
> therefore, rather closer to the totally repetitive end of the scale than 
> to the one shot end of the scale.
> 
> Regards,
> Srece

But if the quantisation noise is repetitive this would happen only when 
there is more than merely 'a lot of similarity.'  The signal would have 
to consist of repeating waveforms that are identical down to the one-bit 
level and lower.  This can only happen with a constant-level test-tone 
is present, and only if its frequency is a simple fraction of the sample 
rate.

I suppose a music synthesiser can achieve this, but it would have to be 
a simple one without a touch-sensitive keyboard, and without vibrato or 
tremolo effects and without any accompanying instruments.   With music 
like that, who cares if there are a few harmonically-related spurs 
present?  They may be an improvement!   :=)

Regards,
John

John Monro wrote:
> I don't understand this because I can't see that adding more noise to
> the signal is going to help.

It's not the difference between adding noise and not adding noise.
It's the difference between adding one type of noise (quantization)
and adding two types of noise (dither + quantization).  It turns
out that adding the second type of noise cancels out some of the
bad effects of the first type of noise (by retaining more information
in a large enough sequence of samples).  But both add noise, so
sometimes it's a preference for which combination of noise seems
worse.  In many cases, noise which causes a small signal to suddenly
disappear is far more noticeable than noise that causes a small
signal to fade gradually into the a bit more background noise.


IMHO. YMMV.
-- 
rhn A.T nicholson d.0.t C-o-M