From: Chuck Simmons
Organization: You jest.
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Subject: Re: DSP 2's complement vs straight binary
References: <3DB2D0B6.5CB0B39B@webaccess.net> <email@example.com> <3DB3882C.5207BE6A@webaccess.net> <firstname.lastname@example.org>
Date: Tue, 22 Oct 2002 12:03:30 GMT
NNTP-Posting-Date: Tue, 22 Oct 2002 05:03:30 PDT
John Larkin wrote:
> On Mon, 21 Oct 2002 04:53:26 GMT, Chuck Simmons
> >StevJensen wrote:
> >> Chuck Simmons email@example.com
> >> >Actually, the LSBs are somewhat useful in a noisy environment. They tend
> >> >to average to the correct result as long as the noise is uncorrelated.
> >> >In designing IIR filters and integrators, this is useful to know about.
> >> >Even though I cascade second order filters to avoid extreme coefficient
> >> >sensitivity and roundoff problems in fixed point implementation, I still
> >> >get some benefit from noise. This is particularly true in closed loop
> >> >systems where noise prevents limit cycling around zero.
> >> Interesting. I vaguely recall a research article that IIRC discussed doing just
> >> this.
> >> Introducing a noise source to lower the overall noise of the system.
> >Yes, this is the case. The usual method of modeling A/D quantization is
> >as a noise source (I think you can find that in Franklin and Powell but
> >I can't remember the title - I can't find my copy so it is probably in
> >my desk at work). But quantization is not stochastic so the model is not
> >awfully good unless uncorrelated system noise is large enough to make
> >quantization more random. This works well enough that I usually use at
> >least two guard bits below the LSB of the A/D in calculation. If the
> >system noise, however, is too large, I end up with the same problems I
> >would have in a continuous time linear analog system. I reserve the word
> >"ugly" for that.
> The nuclear spectroscopy folks like to add noise (generated by a DAC)
> to their signals, then subtract it out digitally after the ADC. They
> use LOTS of noise, not just a few LSBs. This allows pretty histograms
> to be made with fast ADCs that have mediocre differential linearlty.
You mentioned that in a related thread a couple of weeks ago or so. In
that application, it makes a lot of sense. In closed loop systems, it is
not quite as attractive because of the added complexity without nearly
as much improvement as you get. This is partly because I put a rather
tight DNL spec on the A/D in the vicinity of the mid code and greatly
relaxed the INL spec, The A/D designer was able to work with this and,
indeed, the INL is pretty bad with lots of droop at the ends.
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons firstname.lastname@example.org