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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?
References: <email@example.com> <3DB2E3CE.firstname.lastname@example.org> <email@example.com> <3DB41488.firstname.lastname@example.org> <3DB43497.A32B8380@webaccess.net> <3DB45343.E61C1CCB@webaccess.net> <3DB466BC.593D4D35@webaccess.net> <3DB5452A.B792F3AC@webaccess.net> <3DB55886.9865D8D1@webaccess.net> <3DB89837.5FFFA3BF@webaccess.net>
Date: Fri, 25 Oct 2002 13:32:16 GMT
NNTP-Posting-Date: Fri, 25 Oct 2002 06:32:16 PDT
Kevin Aylward wrote:
> "Chuck Simmons" wrote in message
> > Kevin Aylward wrote:
> > >
> > > "Chuck Simmons" wrote in message
> > > news:3DB55886.9865D8D1@webaccess.net...
> > > > Kevin Aylward wrote:
> > > > >
> > > > > The mathematics "prove" that there is an inherent measurement
> > > problem in
> > > > > the real world. You cannot measure frequency 100% accurately,
> > > without
> > > > > taking infinite time.
> > > >
> > > > No, you are reversing the implication. The "proof" of your
> > > > requires inserting an underlying physical context which is not in
> > > > mathematics. The physical context spuriously inserted is physical
> > > > measurement error.
> > >
> > > You misunderstand the basics. The uncertainty relation
> > > nothing to do with a physical measurement error, in the sense of
> > > imperfect equipment. The assumption is that the measuring equipment
> > > ideal. The issue is with the representation of signals.
> > I do not misunderstand the basics.
> Yes you do. You do not understand that short pulses require large BW.
> 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
> I explained in another reply to one of your posts that noise is not
> e.g. short pulse require large BW, so that pulse width*BW is not
> arbitrary. The shorter the pulse, the larger the BW, i.e. short pulses
> have large Fourier transform spreads, and long pulses have narrow BW,
> i.e, if you require a narrow BW, i.e. to measure a frequency accurately,
> it takes a lot of time.
> This is expressed by Sigma_F * Sigma_T >=1/2. The standard deviations
> are determined by the shape of the pulse and the shape of the pulses
> Fourier transform. Noise is not involved at all.
The difficulty here is that standard deviation is pretty meaningless in
the absence of noise. In fact, it is zero identically. The references
you gave earlier in one case introduced noise and in the other
uncertainty was simply assumed to exist if intervals are truncated.
Quite clearly, if I give you the following function:
f(t)=sin(t) for all t in 0
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