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From: email@example.com (john jardine)
Subject: Re: How does a mixer work?
Date: 25 Oct 2002 09:34:49 -0700
NNTP-Posting-Date: 25 Oct 2002 16:34:49 GMT
"Kevin Aylward" wrote in message news:...
> "john jardine" wrote in message
> > "Kevin Aylward" wrote in message
> > > "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
> > > > incompatible by its uncertainty relation Sigma.Sigma >=1/2. And in
> > > 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"
> (in this
> > form, cant find any, other than re wavelets)
> Ahmmm. I did explain in one of the other posts. This equation is
> *absolutely* bog standard. Its in any reasonable text book on signal
> analysis. Its called the time frequency uncertainty relation. It forms
> the mathematical basis of the Hiesenburg uncertainty relation.
> Consider a pulse of arbitrary shape in the time domain. Calculate its
> standard deviation of its time width, call this Sigma_T. Take the
> Fourier transform of this pulse. Calculate its standard deviation of its
> frequency width. It can be shown that the product of these two standard
> deviations is always greater or equal to 1/2. The equal condition is for
> the gaussian pulse, which has the same Fourier transform, exp(-t^2/2).
> This equation formalises the notion that it is impossible to know both
> f(t) and g(w) to an arbitrary degree of precision. Intuitively it should
> be obvious. If you want to measure frequency more accurately, you need
> to measure of a longer time period.
> Kevin Aylward
> SuperSpice, a very affordable Mixed-Mode
> Windows Simulator with Schematic Capture,
> Waveform Display, FFT's and Filter Design.
Cheers!. Makes sense now. Yes, I suppose in his way, Gabor was stating
the obvious. Can now put it in the "tending towards infinity or
Planc's limit" drawer.
ps. Unless you've an executive service from google, you chaps must be
plugged in 24/7. some of us mortals need *sleep*!.
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