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From: Chuck Simmons
Organization: You jest.
X-Mailer: Mozilla 4.61 [en] (X11; U; Linux 2.0.33 i586)
Subject: Re: How does a mixer work?
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Date: Fri, 25 Oct 2002 01:03:13 GMT
NNTP-Posting-Date: Thu, 24 Oct 2002 18:03:13 PDT
Kevin Aylward wrote:
> "Chuck Simmons" wrote in message
> > Kevin Aylward wrote:
> > >
> > > The mathematics "prove" that there is an inherent measurement
> problem in
> > > the real world. You cannot measure frequency 100% accurately,
> > > taking infinite time.
> > No, you are reversing the implication. The "proof" of your statement
> > requires inserting an underlying physical context which is not in the
> > mathematics. The physical context spuriously inserted is physical
> > measurement error.
> You misunderstand the basics. The uncertainty relation (Dt.Df>=1/2)has
> nothing to do with a physical measurement error, in the sense of using
> imperfect equipment. The assumption is that the measuring equipment is
> ideal. The issue is with the representation of signals.
I do not misunderstand the basics. The uncertainty relation introduces a
physical context by adding noise to the signal. Noise is not a
mathematical concept precisely except that it is considered in
probability theory and statistics. I never ran accross noise in the
study of harmonic analysis. I would have considered it very strange if
it had. Generally speaking (mathematics hat on my head) noise is
uninteresting and does not belong in analysis at all simply because it
is orthogonal to the study of analysis. What place would it have in a
course on point set topology and functional analysis? None so it is not
found there. What possible sense would there be in bringing in niose in
a course in harmonic analysis? None because it is not part of Fourier
analysis at all. However, when you bring in a physical context
(sometimes done in applied math courses), noise may be relevant.
I've personally had very little contact with applied mathematics (of the
sort where you drag in physics and so forth) since I'm not interested in
it. This is why I have never seen your uncertainty relation. It is quite
possible for a mathematics graduate student specializing in harmonic
analysis to get a PhD without ever seeing the uncertainty relation. It
is certainly not in any of the 30 or 40 mathematics books I have which
deal, to some degree, with Fourier transforms.
> In one case a signal is being characterised in the frequency domain, and
> in the other the signal is being characterised in the time domain. The
> mathematics show that these domains are not completely compatible.
Perhaps but only if you introduce a physical context. That is the only
way you can bring in uncertainty. It appears that I understood you
exactly and you did not understand what I said.
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons email@example.com
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