Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <3DB41488.email@example.com> <3DB43497.A32B8380@webaccess.net> <3DB45343.E61C1CCB@webaccess.net> <3DB466BC.593D4D35@webaccess.net> <3DB73CD9.D99E28FF@webaccess.net>
Subject: Re: How does a mixer work?
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Date: Thu, 24 Oct 2002 08:07:45 +0100
NNTP-Posting-Date: Thu, 24 Oct 2002 08:07:53 BST
"Chuck Simmons" wrote in message
> Kevin Aylward wrote:
> > "John Woodgate" wrote in message
> > news:TeLxB9BOKst9EwnI@jmwa.demon.co.uk...
> > > I read in sci.electronics.design that James Meyer
> > > wrote (in
> > > > firstname.lastname@example.org>) about 'How does a mixer work?', on Wed, 23 Oct 2002:
> > >
> > > > Correct! Since a Dirac pulse contains all the information
> > known, or
> > > >which will be known; all the transmissions that have ever been
> > produced, or will
> > > >be produced, are redundant.
> > >
> > > Well, not quite correct, because no-one has ever produced a Dirac
> > pulse.
> > > We are waiting for some transistors with infinite Vcbo. (;-)
> > Well, not even that. A dirac pulse contains no useful information.
> > certainly true that for a signal to have information content it must
> > have some randomness associated with it, i.e. log2(/pi), and that as
> > consequence, a random signal has a frequency spectrum. It does not
> > necessarily follow that anything with a complete spectrum contains
> > useful information. White noise, is just that, white noise.
> It's worse. It is trivial to prove that there does not exist a
> integrable function having the properties of the "Dirac delta." The so
> called approximating sequences are all divergent and therefore do not
> converge to any function. In short, there does not exist a function
The Dirac function, as you say is not a function. It is a distribution.
It can be treated entirely rigorously as a limit of a sequence of
integrals. Agreed, the limit of the sequences themselves diverge, but
this is not relevant. Its the limit of the integral that matters (e.g.
Mathematical Methods for Physicists - Arfken, p.84-88) The Dirac
sequence (function) has no technical meaning outside of an integral.
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