🚀 go-pugleaf

In article <92215.104659MIWHC@CUNYVM.BITNET> MIWHC@CUNYVM.BITNET writes:
> [asks for help with "practical" aspects of Fourier transforms]


Numerical Recipes (Press, Flannery, Teukolsky, and Vetterling,
Cambridge) has a lot of really nice explanations in their
Fourier transform chapter (and others, too).  They also have a good
annoted bibliography to help you dig deeper if that's necessary.

Kahaner, Moler, and Nash ("Numerical Methods and Software", Prentice-Hall)
have more examples [and a nice 1-page capsule bibliography of Fourier
-- did you know that he played a major role in inspiring Champollion
to take up the studies which lead to his decrypting the Rosetta stone
(Egyptian hieroglyphics)?], but a slightly less "physicist in the
trenches" approach than NR, and no annotations in their bibliography.

I (highly) recommend both of these books -- they complement each
other, often one will clarify a point the other leaves slightly
unclear.  To help in *understanding* what's going on with Fourier
transforms, read the chapters in both books.


Both books also include actual codes, NR in your choice of Fortran,
C, or Pascal, KMN in Fortran.  I'm not an expert in Fourier transforms,
so I can't assess their quality.  However, other NR codes have often
turned out to be of moderate or even poor quality, so I'd be a bit
dubious of using their Fourier codes without an independent expert's
favorable review.  In contrast, so far as I know the expert reviews
of (other) KMN codes have all been quite favorable.

I'd recommend the KMN codes to start with, since they give examples
for their use.  But there are also a lot of other Fourier codes around,
eg see netlib.  I have no specific knowledge of the quality of any
of these codes, but netlib stuff is generally excellent.


- Jonathan Thornburg
  <jonathan@einstein.ph.utexas.edu> or <jonathan@hermes.chpc.utexas.edu>
  University of Texas at Austin / Physics Dept / Center for Relativity
  and (for a few more months) U of British Columbia / {Astronomy,Physics}