"Matt Timmermans" <mt0000@sympatico.nospam-remove.ca> wrote in message news:<O3PVa.4088$537.656342@news20.bellglobal.com>...
> "Randy Yates" <yates@ieee.org> wrote in message
> news:3F272526.DC84F022@ieee.org...
> > I have some material on
> > analyzing stability at work - I'd be happy to provide the references when
> > I get in tomorrow if you're interested.
>
> Yes, please ;-)
Okie dokie, Matt. Here is a list of articles I've collected on delta
sigma conversion in general, not just stability. I have the electronic
forms so if you email me at randy.yates@sonyericsson.com I can attach
and send them to you:
1. "Stability Analysis of the Second Order Sigma Delta Modulator," Philip
Steiner and Woodward Yang, Division of Applied Sciences, Harvard;
2. "A Higher Order Topology for Interpolative Modulators for Oversampling
A/D Converters," Chao, Nadeem, Lee, and Sodini, IEEE Transactions on Circuits
and Systems, vol. 37, no. 3, March 1990.
3. "An Empirical Study of High-Order Single-Bit Delta-Sigma Modulators,"
Richard Schreier, IEEE Transactions on Circuits and Systems, vol. 40, no. 8,
August 1993.
4. "Effective Dithering of Sigma-Delta Modulators," Steven R. Norsworthy,
AT&T Bell Laboratories,
5. "A Comparison of Dithered and Chaotic Sigma-Delta Modulators," Chris
Dunn and Mark Sandler, JAES, April 1996.
6. "Psychoacoustically Optimal Sigma Delta Modulation," Chris Dunn and
Mark Sandler, JAES, April 1997.
Reply by Mark Ovchain●July 30, 20032003-07-30
kbc32@yahoo.com (kbc) wrote in message news:<a382521e.0307280611.7dbc8958@posting.google.com>...
> I am finding the sigma-delta adc difficult to understand.
>
> The only way, i feel, to reduce the quantization noise ,
> given the bit-resolution , is to sample non-uniformly.
>
> Is that what happens ?
>
> shankar
No, that's not what happens.
What one does is to oversample by a lot, and use noise-shaping
filters. This means that you can move the quantization noise way up in
frequency, where it doesn't matter, and then take it out with a simple
filter.
Look in Jayant and Noll at "A*PCM".
Reply by Matt Timmermans●July 30, 20032003-07-30
"Randy Yates" <yates@ieee.org> wrote in message
news:3F272526.DC84F022@ieee.org...
> Hi Matt,
>
> I wasn't clear when I stated "digital signal." What I meant was a signal
> that is digitized (or re-digitized) using a simple N-bit quantizer. The
> noise is about 6*N dB below the full-scale signal.
You were clearer than I was, I think. My concern is that this only holds as
long as the input is inside the full scale range of the quantizer. In the
S-D modulator, the quantizer is quantizing the feedback, and I can't find a
mechanism that limits the feedback to that range, even if the input signal
is guaranteed to be so limited.
> I believe what you are talking about is the stability of the modulator
> due to the feedback loop.
Right, but stability isn't quite sufficient. Certain inputs may be
amplified by the quantizer enough to drive the feedback outside of the
quantizer's input range. At that point, the quantization noise increases
with the feedback magnitude, or, more likely, the feedback hits a supply
rail and the analysis goes out the window.
> That's a whole other subject and one that is
> quite complex from what I've gathered. I think they've analyzed first-
> and second-order loops analytically for stability, but higher-order
> loops are still a shot in the dark (I think). I have some material on
> analyzing stability at work - I'd be happy to provide the references when
> I get in tomorrow if you're interested.
Yes, please ;-)
Reply by Randy Yates●July 29, 20032003-07-29
Matt Timmermans wrote:
>
> You know, I think S-D modulators are designed incorrectly.
>
> The goal should be to minimize the power of the real quantization noise,
> defined as modulator output minus input signal, after passing through a
> reconstruction filter.
Yeah, well that's a heckuva minimization problem. Is there only one
minimum? What does the performance surface look like? Interesting
idea - lots of questions in the how-to-do category.
> This can be viewed as an adversarial game played between the modulator,
> which gets to choose the sign of the noise pulse produced in every sample
> period, and the input signal, which gets to (within bounds) choose the
> magnitude.
>
> In general, I don't think that the modulator's optimal strategy would be to
> simply quantize a LTI function of the input signal. Instead, a more
> compilcated function would partition the state space of the reconstruction
> filter into 1 and -1 output regions. The modulator's best strategy would be
> equivalent to simulating the reconstruction filter and applying this
> decision procedure on its state.
>
> Hmmm...
>
> Matt
Hmmm...
--
% Randy Yates % "...the answer lies within your soul
%% Fuquay-Varina, NC % 'cause no one knows which side
%%% 919-577-9882 % the coin will fall."
%%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr
Reply by Randy Yates●July 29, 20032003-07-29
Matt Timmermans wrote:
>
> "Randy Yates" <yates@ieee.org> wrote in message
> news:3F25E9A0.6651F163@ieee.org...
> > The quantization noise power in a digital signal is constant no
> > matter what the sample rate is.
>
> I have tried, but I haven't been able to show this for >= 2 stage S-D
> modulators. The trouble is that, while the digital stream has limited
> power, there doesn't seem to be any bound on the *error* signal it's
> digitizing, and so there is no limit on the difference between the two!
>
> I know they don't go too unstable in practice, but how do we get an estimate
> on the maximum error signal?
Hi Matt,
I wasn't clear when I stated "digital signal." What I meant was a signal
that is digitized (or re-digitized) using a simple N-bit quantizer. The
noise is about 6*N dB below the full-scale signal.
I believe what you are talking about is the stability of the modulator
due to the feedback loop. That's a whole other subject and one that is
quite complex from what I've gathered. I think they've analyzed first-
and second-order loops analytically for stability, but higher-order
loops are still a shot in the dark (I think). I have some material on
analyzing stability at work - I'd be happy to provide the references when
I get in tomorrow if you're interested.
--
% Randy Yates % "...the answer lies within your soul
%% Fuquay-Varina, NC % 'cause no one knows which side
%%% 919-577-9882 % the coin will fall."
%%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr
Reply by Matt Timmermans●July 29, 20032003-07-29
You know, I think S-D modulators are designed incorrectly.
The goal should be to minimize the power of the real quantization noise,
defined as modulator output minus input signal, after passing through a
reconstruction filter.
This can be viewed as an adversarial game played between the modulator,
which gets to choose the sign of the noise pulse produced in every sample
period, and the input signal, which gets to (within bounds) choose the
magnitude.
In general, I don't think that the modulator's optimal strategy would be to
simply quantize a LTI function of the input signal. Instead, a more
compilcated function would partition the state space of the reconstruction
filter into 1 and -1 output regions. The modulator's best strategy would be
equivalent to simulating the reconstruction filter and applying this
decision procedure on its state.
Hmmm...
Matt
Reply by Matt Timmermans●July 29, 20032003-07-29
"Jerry Avins" <jya@ieee.org> wrote in message
news:3F267E28.CBE24859@ieee.org...
> Although it may not be possible to know the upper bound of the error in
> any one sample (other than that imposed by dynamic range), the feedback
> and the band-limited input together bound the short-term average error
> to a reasonable amount. After all, the buggers do work!
Interesting that you mention a band-limited input. I have a feeling that
this is important for their stability and good performance. Even though it
isn't a part of the standard analysis, a band-limited input rules out
adversarial sorts of input signals that might try to maximize the magnitude
of the feedback term.
Reply by Mahesh Godavarti●July 29, 20032003-07-29
Think of a slowly varying signal. Instead of quantizing each sample of
this signal how about quantizing the difference of two samples. The
dynamic range is lower and you would need fewer bits. Reconstruct the
sampled version of the original signal by doing the inverse of the
difference.
This is in essence what sigma-delta converters do.
Jerry Avins <jya@ieee.org> wrote in message news:<3F267E28.CBE24859@ieee.org>...
> Matt Timmermans wrote:
> >
> > "Randy Yates" <yates@ieee.org> wrote in message
> > news:3F25E9A0.6651F163@ieee.org...
> > > The quantization noise power in a digital signal is constant no
> > > matter what the sample rate is.
> >
> > I have tried, but I haven't been able to show this for >= 2 stage S-D
> > modulators. The trouble is that, while the digital stream has limited
> > power, there doesn't seem to be any bound on the *error* signal it's
> > digitizing, and so there is no limit on the difference between the two!
> >
> > I know they don't go too unstable in practice, but how do we get an estimate
> > on the maximum error signal?
>
> Fools rush in, and all that. At the risk of piling foolishness on
> ignorance, I hazard a guess.
>
> Although it may not be possible to know the upper bound of the error in
> any one sample (other than that imposed by dynamic range), the feedback
> and the band-limited input together bound the short-term average error
> to a reasonable amount. After all, the buggers do work!
>
> Jerry
Reply by Jerry Avins●July 29, 20032003-07-29
Matt Timmermans wrote:
>
> "Randy Yates" <yates@ieee.org> wrote in message
> news:3F25E9A0.6651F163@ieee.org...
> > The quantization noise power in a digital signal is constant no
> > matter what the sample rate is.
>
> I have tried, but I haven't been able to show this for >= 2 stage S-D
> modulators. The trouble is that, while the digital stream has limited
> power, there doesn't seem to be any bound on the *error* signal it's
> digitizing, and so there is no limit on the difference between the two!
>
> I know they don't go too unstable in practice, but how do we get an estimate
> on the maximum error signal?
Fools rush in, and all that. At the risk of piling foolishness on
ignorance, I hazard a guess.
Although it may not be possible to know the upper bound of the error in
any one sample (other than that imposed by dynamic range), the feedback
and the band-limited input together bound the short-term average error
to a reasonable amount. After all, the buggers do work!
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Matt Timmermans●July 29, 20032003-07-29
"Randy Yates" <yates@ieee.org> wrote in message
news:3F25E9A0.6651F163@ieee.org...
> The quantization noise power in a digital signal is constant no
> matter what the sample rate is.
I have tried, but I haven't been able to show this for >= 2 stage S-D
modulators. The trouble is that, while the digital stream has limited
power, there doesn't seem to be any bound on the *error* signal it's
digitizing, and so there is no limit on the difference between the two!
I know they don't go too unstable in practice, but how do we get an estimate
on the maximum error signal?