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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: fft in hc11 again
Date: Sun, 13 Oct 2002 12:29:25 GMT
NNTP-Posting-Date: Sun, 13 Oct 2002 05:29:25 PDT
John Woodgate wrote:
> I read in sci.electronics.design that Chuck Simmons
> wrote (in <3DA8A583.17B233A3@webaccess.net>)
> about 'fft in hc11 again', on Sat, 12 Oct 2002:
> >Data interpretation is further complicated by misconceptions. Too many
> >engineers think of the DFT and the FFT as giving results that relate to
> >the Fourier transform on the real line. Actually, the FFT and the DFT
> >give results identical to a truncated Fourier transform on the unit
> >circle. I've seen engineers chase wild geese for weeks because they
> >didn't understand that fundamental fact.
> I'm sure you are right, but that's because the level of math knowledge
> required to understand what you wrote there is really quite high. Any
> one who understands a bit about integral calculus can understand Fourier
> analysis, but to understand, particularly, what you mean by 'Fourier
> transform on the unit circle' requires quite a bit of understanding of
> calculus on the complex plane, and many electronics engineers don't get
> that far in math. To understand the implications of that phrase and the
> effects of truncation requires even more depth of knowledge.
I wonder about that. After all, the Fourier trnasform on the unit circle
is simply the Fourier series and truncating it is common practice.
Connecting the result from a DFT to a Fourier series rather than
accusing it of being an approximation of a Fourier transform with
infinite integration limits seems to be the point where some engineers
stumble. It is the latter that has the bear traps and other hazzards
while the former interpretation is more friendly. There are a few books
that deal with the finer points of Fourier techniques in engineering.
There is a certain irony in the way I come to know a bit of mathematics.
What ultimately drove me to study at a university was precisely my
mistrust of mathematical interpretations by fellow engineers.
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons firstname.lastname@example.org
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