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Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <email@example.com> <3DB7ECD5.6F50721E@webaccess.net>
Subject: Re: How does a mixer work?
X-Newsreader: Microsoft Outlook Express 6.00.2800.1106
Date: Thu, 24 Oct 2002 15:03:18 +0100
NNTP-Posting-Date: Thu, 24 Oct 2002 15:03:21 BST
"Chuck Simmons" wrote in message
> Kevin Aylward wrote:
> > "JD" wrote in message
> > news:lhIt9.489$S4.firstname.lastname@example.org...
> > >
> > > "Kevin Aylward" wrote in message
> > > news:FABt9.3089$Af5.email@example.com...
> > > > "JD" wrote in message
> > > > news:JcAt9.474$S4.firstname.lastname@example.org...
> > > > >
> > > > > "Kevin Aylward" wrote in message
> > > > > news:Lkrt9.510$Af5.email@example.com...
> > > > > > "John S. Dyson" wrote in message
> > > > > > news:felt9.436$S4.firstname.lastname@example.org...
> > > > > > >
> > > > > > > "Dbowey" wrote in message
> > > > > > news:email@example.com...
> > > > > >
> > > > > > > I am NOT making the cosmological assertion that everything
> > > > really
> > > > > > > an f(t) or other such off-topic concerns, but am clearly
> > stating
> > > > that
> > > > > > much
> > > > > > > of our real-world that we normally see (in the sense of
> > > > > > discussion)
> > > > > > > is an f(t). f(w) or f(s) is a convienience, where
> > > > > > operations
> > > > > > > or changing signal characteristics can cause some traps
> > > > > > 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
> > > > reality
> > > > > > are just that models, f(t) is no more valid then any other
> > model.
> > > > > >
> > > > > Using LINEAR transforms for modeling nonlinear processes is
> > > > > the incompetency resides.
> > > >
> > > > This simple is not true. Nonlinear processes just make it a bit
> > > > complicated. The issue is one of a fundermental nature,
> > of
> > > > whether the system is complicated or not. "scientific theories
> > the
> > > > 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
> > > might be approximations of something further down.)
> > >
> > The problem here though is the very *definition* of time. It simple
> > not be done with recourse to observation of a motion that is
> 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
> line up with the seasons of the year.
This is a bit misleading. Time increments themselves (the standards) are
not dependant on astronomical events at all. The second is defined as so
many oscillations of such and such an element. It never changes.
However, clocks are reset to get things to line up more conveniently.
> > So, the time domain is still no better then the frequency domain.
> > not an approximation to the frequency domain because its very
> > inherently depends on the frequency domain.
> This sentence appears to contradict the first. Was the first not set
> down properly?
Ok, there is a bit of confusion in the prose here. The original post was
"...they [frequency] are approximations to the time domain". My reply
was addressing that since time is defined by a frequency, frequency can
not be a mere approximation to time.
> However, on the whole, there is nothing about the Fourier
> 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
> 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
> in the statement of conditions on the function. More generally, the
> fourier transform has nothing to do with frequency.
Granted, the Fourier transform itself is indeed just another integral
transform, and as such the variables do not have to be time. Indeed, the
Fourier transform can be used to solve various differential equations
unrelated to time. However, I feel that this is splitting hairs in the
current context. In this context, the variables under discussion are
time and frequency.
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
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