🚀 go-pugleaf

In article 104659MIWHC@CUNYVM.BITNET, <MIWHC@CUNYVM.BITNET> () writes:
>     The undergraduate and grad physics department of my school taught me all
>sorts of stuff about Fourier Transforms for several years. The problem is that
>all I was ever taught was APPLIED crap. I now know how to follow proofs as to
>how a Fourier Transform can prove the existence of mouldy Jell-O, but I am lost
>in applying a reasonably simple transform to a data set with real numbers.
>     Specifically, all I want to do is use the Fast Fourier Transform to scrape
>some usefull data out of some geophysical measurements. I am using Scientists
>Spreadsheet which should do the trick, but my education has left me unprepared
>to know what the output should look like, or mean in the real world of rift
>measurements.
>     If anyone has done this, I would appreciate some advice.

Given a "random" time sequence, the fourier transform returns a frequency-domain
representation of the sinusoids that make up that sequence. The magnitude of
the fourier transform is known as the "spectral" magnitude and is taken
from the output of a complex FT as sqrt( a^2 + b^2 ) per every complex
point in the transform, while the phase component of the transform is
given as arctan( b/a ) for every complex valued point in the transform.
Together, the magnitude and the phase specify the "spectral" makeup of
a given waveform. -For instance, given a signal made up of the additive
addition of two sinusoids (assume sines for simplicity's sake), the
magnitude of the fourier transform of this conglomerate signal would
theoretically give an impulse in the frequency-domain for each fundamental
sinusoid making up the conglomerate whole. -This would be true except for
the effects of finite-sampling which cause the FT to have less accuracy than
if there were infinite sampling. The effect of this finite sampling is to
produce less than perfect impulses at the frequencies making up the comglomerate
waveform.

I have seen another posting concerning this message, and the author of that
message was absolutely correct in recommending the Numerical Recipes book
to you. -I have used the FFT implementations from the NR book for a few years
now with some minor modifications.

One thing to keep in mind in your "search for knowledge" of this subject
is that there are quite a few algorithms available for computing a 
"Fast Fourier Transform". -All should basically give you the same information,
but the algorithms are different in nature (examples: Decimation-in-time,
Decimation-in-frequency, Winograd, prime-factors alg., -others).

Another good book for this, (what many refer to as "the Bible" of DSP),
is the Oppenheim and Shafer "Digital Signal Processing" book from 1975,
or their newer follow-on book "Discrete-time Signal Processing."

-Both books provide in-depth coverage of several of the prevalent FFT
algorithms, as well as more coverage of DFT theory in general. Some
psuedo-code is also provided which is very helpful in implementing the
DIT (Decimation-in-time) and DIF (Decimation-in frequency) FFT implemetations.

-Hope this helps.
-Benjamin Bryant
<bdbryan@eng.clemson.edu>