References: <email@example.com> <3DB68771.7D6EFC53@webaccess.net>
Subject: Re: How does a mixer work?
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Date: Wed, 23 Oct 2002 12:10:26 -0500
NNTP-Posting-Date: Wed, 23 Oct 2002 11:47:00 EST
"Chuck Simmons" wrote in message news:3DB68771.7D6EFC53@webaccess.net...
> John Woodgate wrote:
> > I read in sci.electronics.design that John S. Dyson
> > wrote (in ) about 'How does a mixer
> > work?', on Tue, 22 Oct 2002:
> > > Additionally,
> > >the
> > >normal linear transforms (where spectrum analysis is allied to the fourier
> > >kind of transform) don't generally work well WRT nonlinear operations (or
> > >with signals that have time varying characteristics.)
> > Again, this is confused and misleading. You can certainly, for example,
> > do Fourier analysis on a half-wave or full-wave rectified sine wave,
> > which is the result of a non-linear process.
> I think he is refering to the problem familiar to servo engineers having
> to do with instrumental methods of Fourier analysis. In particular, some
> dynamic analyzers use white noise to excite a system, collect data for a
> time, then apply a DFT and finally display the result. This is
> unworkable on many servo systems because the spectrum that results is
> highly polluted with modulation products that are of no interest
> whatever. Much more meaningfull results are obtained using swept sine
> excitation and using single point DFTs at frequency points in the sweep.
> This eliminates meaningless garbage from the spectrum. Dynamic analyzers
> from Agilent and SRS of the better sort have swept sine available.
Note also, that the real world nonlinear devices will also pollute the spectrum.,
Much of the world is chaotic and nonlinear, and trying to model it with
linear transforms (in general) is foolhardy. That doesn't mean that there
are specific cases where linear transforms and models using ergodic functions
cannot be useful, but it does mean that they aren't sufficient (in general.)
If someone can develop a full theory of a nonlinear fourier transform that is
as easy to understand as the f(t) nonlinear domain, then the nonlinear frequency
domain becomes more useful (in general.) We can certainly conceptually
pattern match the nonlinear behavior in the frequency domain, but that
is a 'technicians view', akin to an engineers helper.