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From: Chuck Simmons
Organization: You jest.
X-Mailer: Mozilla 4.61 [en] (X11; U; Linux 2.0.33 i586)
Subject: Re: Fourier doesn't do nonlinear very well
Date: Thu, 24 Oct 2002 03:12:23 GMT
NNTP-Posting-Date: Wed, 23 Oct 2002 20:12:23 PDT
> "John Woodgate" wrote in message
> > I read in sci.electronics.design that JD wrote (in
> > ) about 'How does a mixer work?', on
> > Wed, 23 Oct 2002:
> > >Perhaps you choose to be misled?
> > I see. You are just a troll. I'm not playing.
> Actually, your comment was the troll... Refer carefully the RUDE
> comment that was made by you. I responded to you, and I guess
> that my mistake was to assume that you sometimes have good manners.
> The fact is that the world
> is mostly nonlinear diffeqs, and it is really incompetent (amazingly
> so) that real world EEs try to always think that Fourier can work
> in that environment.
> The most amazing thing to me, again, is that you guys were
> arguing about something that is so obvious...
I don't want to get into this troll business.
I don't think that anyone will argue with you about nonlinear behavior
in garden variety situations. Part of choosing a model for a system is
making decisions about the accuracy required - at least in engineering
situations. It often happens that nonlinearities are small enough that
one can use a linear model without much risk in achieving a goal. One
must apply some thought to measuring a system in such a way that the
data can usefully be used to varify the model and proceed with a design
or whatever is desired.
I have for years been dealing with discrete time quantized systems
(digital control of dynamics). These are nonlinear if you look at them
in continuous time. However, there are various linear methods that make
life easier. Actually, time domain techniques are often used in this
because there are particularly nice matrix methods that are powerful
design tools. It should not come as a complete shock that system
stability falls out of examining the eigenvalues of certain matrices
exactly like in linear continuous time systems.
It is a bonus that such systems also admit continuous linear methods for
performance analysis after design is complete. Part of making this all
work is understanding how significant nonlinearities are. For a great
many systems, nonliearities are not seriously in the way of doing fairly
simple design and analysis (don't spread that around or I'll be out of a
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons email@example.com
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