# Noise Shaping and Clipping

Started by October 12, 2008
```Consider a requantization system with noise shaping and dithering.
The question is what to do when the sum of the signal, the noise
feedback and dither exceeds the range of the output quantizer.
A differentiator of the Nth order used as a noise shaping filter has the
max. feedback of ~2^N. So it is quite likely that the quantizer will run
out of range at or near the peak values of the input signal.

I can see the following approaches to this problem:

1) Limit the input signal so the requantizer will never run out of
range. This works, however it reduces the available dynamic range. The
reduction can be substantial if the noise shaping of high order is used.

2) Limit the sum of signal, dither and noise feedback to +/-max of the
output quantizer. Calculate the feedback taking this limiting into the
account. The result is horrid; error windup.

3) Limit the sum to +/- max. output, set the feedback to +/- 1 lsb
accordingly.

What do you think is right approach?

DSP and Mixed Signal Design Consultant
http://www.abvolt.com
```
```On Sun, 12 Oct 2008 10:00:56 -0500, Vladimir Vassilevsky
<antispam_bogus@hotmail.com> wrote:

>What do you think is right approach?

1) and 3) represent the classic tradeoff between "make certain that
numerical overflow is impossible" and "make certain that numerical
overflow is rare and handled gracefully when it occurs".  If you have
usually use "engineering judgment" to find a good compromise in case
3) -- possibly along with some form of "soft" clipping -- so that the
occurrences are rare enough and benign enough to pass unnoticed.
Otherwise you have to take the ultra-conservative approach of 1).

I wouldn't use 2) at all, for the reason that you stated.

Greg
```
```Vladimir Vassilevsky wrote:

>
> Consider a requantization system with noise shaping and dithering.
> The question is what to do when the sum of the signal, the noise
> feedback and dither exceeds the range of the output quantizer.
> A differentiator of the Nth order used as a noise shaping filter has the
> max. feedback of ~2^N. So it is quite likely that the quantizer will run
> out of range at or near the peak values of the input signal.
>
> I can see the following approaches to this problem:
>
> 1) Limit the input signal so the requantizer will never run out of
> range. This works, however it reduces the available dynamic range. The
> reduction can be substantial if the noise shaping of high order is used.
>
> 2) Limit the sum of signal, dither and noise feedback to +/-max of the
> output quantizer. Calculate the feedback taking this limiting into the
> account. The result is horrid; error windup.
>
> 3) Limit the sum to +/- max. output, set the feedback to +/- 1 lsb
> accordingly.
>
> What do you think is right approach?

If the whole purpose of this system is digital processing of analog signals,
(meaning analog in, analog out) then another solution would be to use
more bits in the processing chain and the DAC than the ADC provides, and
set the amplification factor of the output stage such that unity gain of
analog signals is garantueed.

bye
Andreas
--
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```
```Vladimir Vassilevsky <antispam_bogus@hotmail.com> writes:

> Consider a requantization system with noise shaping and dithering.
> The question is what to do when the sum of the signal, the noise
> feedback and dither exceeds the range of the output quantizer.
> A differentiator of the Nth order used as a noise shaping filter has
> the max. feedback of ~2^N. So it is quite likely that the quantizer
> will run out of range at or near the peak values of the input signal.
>
> I can see the following approaches to this problem:
>
> 1) Limit the input signal so the requantizer will never run out of
> range. This works, however it reduces the available dynamic range. The
> reduction can be substantial if the noise shaping of high order is
> used.
>
> 2) Limit the sum of signal, dither and noise feedback to +/-max of the
> output quantizer. Calculate the feedback taking this limiting into the
> account. The result is horrid; error windup.
>
> 3) Limit the sum to +/- max. output, set the feedback to +/- 1 lsb
> accordingly.

First of all, are you talking about an N-bit requantizer or a 1-bit
requantizer? I think you mean an N-bit, so that's what I'll assume in
the following.

I'm not sure what you mean by 2). Do you mean to simply feed back the
saturated N bits?

If not, then that would be the fourth, and most reasonable, option, in
my opinion.

In any case, the problem can be modeled as follows. The standard model
for a quantizer is a node that adds noise. If the input signal exceeds
the quantizer's range (and we saturate), then what changes is the nature
/ statistics of that noise. For one, the range of the noise becomes
greater.

So you may be able to resolve your question in these terms.

Note also that a 1-bit quantizer ALWAYS saturates!
--
%  Randy Yates                  % "Bird, on the wing,
%% Fuquay-Varina, NC            %   goes floating by
%%% 919-577-9882                %   but there's a teardrop in his eye..."
%%%% <yates@ieee.org>           % 'One Summer Dream', *Face The Music*, ELO
http://www.digitalsignallabs.com
```
```On Oct 13, 6:11&#2013266080;am, Randy Yates <ya...@ieee.org> wrote:
...
>
> Note also that a 1-bit quantizer ALWAYS saturates!

an important point to repeat.

because of that and that the quantizer is only one step of what would
be a staircase function if it was more than 1-bit, since there is no
other steps in the staircase, you cannot infer a gain from the slope
of the staircase if you were trying to model the quantizer as an
additive noise source.  then it's a little harder to infer the
effective gain of the quantizer (which is something like the mean
absolute value of the input times delta/2, half the step size, divided
by the mean square of the input).

the other important fact to remember is that if you were to put a
linear gain stage (with a positive gain coef) before the 1-bit
quantizer (a.k.a. a comparator), the inherent gain of the comparator
would absorb whatever positive gain you insert.  we know this because
we know that the comparator output would be unchanged (still +/- delta/
2).  if the inherent gain of the comparator did not absorb any
preceding gain, then the linear model of the delta-sigma modulator
would change (and get better) with increased loop gain.  but we know
that increasing the gain there at that part of the loop cannot change
anything.

r b-j
```