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From: "Steven G. Johnson" <stevenj@alum.mit.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Does Matlab do FFT correctly ?
Date: Fri, 2 May 2008 21:14:29 -0700 (PDT)
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On May 2, 6:09 pm, "Chen Sagiv" <chensagiv...@gmail.com> wrote:
> Nevertheless, I will have to argue that this point is not
> clear at all. Most people refer only to the abs of the FT
> anyway, and this problem will simply go un-noticed. Only
> when phase is of interest, you really look at this subtle
> point.

Oh, absolutely.  Fourier transforms are subtle to begin with, and then
when you add discretization etc. on top of that it is a tricky
subject.  Lots of students find it difficult, and digital signal
processing and DFTs are usually a relatively advanced subject in an
university curriculum.  And it's easy to find people online who are
confused about this topic.

However, it's not Matlab's fault, and I don't think there's much that
they can do to eliminate the subtleties of this subject.

(If you think they should shift the origin of the FFT to the center of
the array for you, then think again.  First, doing so would make them
incompatible with the universal convention of textbooks, papers, etc.
on this subject.  Second, it's not a trivial matter to "center" the
origin, since the location of the "center" pixel is ambiguous for even
N; this makes the ifftshift function more tricky to use properly than
it may seem.  Third, it makes the DFT formula more complicated-
looking.  Fourth, the location of the origin is really the least of
the subtleties of the DFT.)

Regards,
Steven G. Johnson