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Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <email@example.com> <firstname.lastname@example.org>
Subject: Re: How does a mixer work?
X-Newsreader: Microsoft Outlook Express 6.00.2800.1106
Date: Thu, 24 Oct 2002 21:06:39 +0100
NNTP-Posting-Date: Thu, 24 Oct 2002 21:06:39 BST
"john jardine" wrote in message
> "Kevin Aylward" wrote in message
> > "Kevin Aylward" wrote in message
> > news:o%Mt9.435$Zk2.email@example.com...
> > > Well, I did explain that the frequency and time domain are
> > fundamentally
> > > 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?.
>Any references on the web?
search on the combined "words time frequency uncertainty relation"
> 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.
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
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