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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: How does a mixer work?
Date: Thu, 24 Oct 2002 12:50:59 GMT
NNTP-Posting-Date: Thu, 24 Oct 2002 05:50:59 PDT
Kevin Aylward wrote:
> "JD" wrote in message
> > "Kevin Aylward" wrote in message
> > news:FABt9.3089$Af5.firstname.lastname@example.org...
> > > "JD" wrote in message
> > > news:JcAt9.474$S4.email@example.com...
> > > >
> > > > "Kevin Aylward" wrote in message
> > > > news:Lkrt9.510$Af5.firstname.lastname@example.org...
> > > > > "John S. Dyson" wrote in message
> > > > > news:felt9.436$S4.email@example.com...
> > > > > >
> > > > > > "Dbowey" wrote in message
> > > > > news:firstname.lastname@example.org...
> > > > >
> > > > > > I am NOT making the cosmological assertion that everything is
> > > really
> > > > > > an f(t) or other such off-topic concerns, but am clearly
> > > that
> > > > > much
> > > > > > of our real-world that we normally see (in the sense of this
> > > > > discussion)
> > > > > > is an f(t). f(w) or f(s) is a convienience, where nonlinear
> > > > > operations
> > > > > > or changing signal characteristics can cause some traps and/or
> > > > > pitfalls
> > > > > > for those who don't deal with the stuff all of the time.
> > > > >
> > > > > I disagree that one view is more real then another. Models of
> > > reality
> > > > > are just that models, f(t) is no more valid then any other
> > > > >
> > > > Using LINEAR transforms for modeling nonlinear processes is where
> > > > the incompetency resides.
> > >
> > > This simple is not true. Nonlinear processes just make it a bit more
> > > complicated. The issue is one of a fundermental nature, ireespectibe
> > > whether the system is complicated or not. "scientific theories are
> > > free creation of the human mind" - Albert Einstien.
> > >
> > The fundamental nature is usually where the problem can be clearly
> > explained. Fourier domain is not such a place for our nonlinear
> > and chaotic world. There certain are frequency domain models for
> > visualization, but they are approximations to the time domain (which
> > might be approximations of something further down.)
> The problem here though is the very *definition* of time. It simple can
> not be done with recourse to observation of a motion that is repetitive.
But has been since the dawn of recorded history. To this day, time
standards are corrected to astronomical events which can be considered
more or less repetitive. The deeper reason is that time measurement must
line up with the seasons of the year.
> So, the time domain is still no better then the frequency domain. It's
> not an approximation to the frequency domain because its very definition
> inherently depends on the frequency domain.
This sentence appears to contradict the first. Was the first not set
However, on the whole, there is nothing about the Fourier transformation
that relates it to frequency. Certainly the definition of it does not.
Like all other integral operators, an interpretation of the result, if
any, depends on the the relationship of the domain of the original
function and the domain of the transformed function. In the case of the
Fourier transform, the domain of the transformed function is not
frequency except in the very limited case of the Fourier transform in
only one dimension when the domain of the original function is a
function of a single variable that is specifically associated with time
in the statement of conditions on the function. More generally, the
fourier transform has nothing to do with frequency.
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons email@example.com
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