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Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <email@example.com> <firstname.lastname@example.org> <3DB88D9C.50F75FA0@webaccess.net>
Subject: Re: How does a mixer work?
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X-Inktomi-Trace: public1-pete2-5-cust19.pete.broadband.ntl.com 1035526203 30990 22.214.171.124 (25 Oct 2002 06:10:03 GMT)
Date: Fri, 25 Oct 2002 07:10:03 +0100
NNTP-Posting-Date: Fri, 25 Oct 2002 07:10:04 BST
"Chuck Simmons" wrote in message
> Kevin Aylward wrote:
> > "john jardine" wrote in message
> > news:email@example.com...
> > > "Kevin Aylward" wrote in message
> > news:...
> > > > "Kevin Aylward" wrote in message
> > > > news:o%Mt9.435$Zk2.firstname.lastname@example.org...
> > > > > Well, I did explain that the frequency and time domain are
> > > > fundamentally
> > > > > incompatible by its uncertainty relation Sigma.Sigma >=1/2.
> > > > view
> > > >
> > > > Sigma_F.Sigma_T>=1/2
> > > That equation looks a bit portentious to me.
> > That's only became you are not familiar with what is quite a basic
> > result. Its pretty fundamental really.
> > >Where did it come from?.
> > A book. Any math text on fourier transforms for example.
> > > Why the ">"?. Who figured it out?.
> > Apparently Gabor.
> > >Any references on the web?
> > search on the combined "words time frequency uncertainty relation"
> > http://www.mathpages.com/home/kmath152.htm
> > http://sepwww.stanford.edu/sep/prof/fgdp/c4/paper_html/node2.html
> Math text books on Fourier transforms, harmonic analysis, analysis,
> functional analysis, differential equations (ordinary and partial),
> integral equations and related areas are very unlikely to have the
> relationship above because noise does not exist in these areas.
Noise is not relevant. You need to try and understand what the relation
> first reference was to sampling which is irrelevant to harmonic
> and both mentioned noise also completely irrelevant to harmonic
> and related mathematical subjects where the Fourier transform is
> mentioned. The proper realm for noise is in statistics which is a
> subject optional for math graduate students (I read probability
> instead). No wonder I never saw it.
These were simple two references are found to illustrate the concept.
The relation itself has nothing to do with noise. It stands on its own.
I don't see why anyone would have an issue with this, its obvious.
Consider a pulse, now make it shorter. The shorter it is the more BW you
need to receive the pulse without distortion. That is, its frequency
spectrum spread gets larger, the shorter the pulse is. If you are not
aware of this, we might as well give up. So, the width of a short pulse
* its BW, is not arbitrary. If one gets smaller, the other must get
larger. If the BW is very short, i.e, you know that the frequency is in
some small range, then it will take a long time to measure it.
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
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