From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: Help w/ Fourier Analysis
Date: 18 Feb 1999 15:53:21 GMT
Newsgroups: sci.math.num-analysis
Keywords: Pointers to Fast Fourier Transform codes

In article <36CC1D2B.95CFC4C5@suntan.eng.usf.edu>,
 elting <elting@suntan.eng.usf.edu> writes:
|>     Does anyone have a set procedure for doing a Fast Fourier
|> Transform?  Suppose I collected 200 data points with the use of a A/D
|> card and the plot of this data was sinusoidal in nature.  How do I use
|> Fourier Analysis to create a mathematical model of this data?  Any
|> advise would be appreciated.
there are lots of codes for doing fft. e.g. 
the library fft  in netlib
(http://www.netlib.org) or
 http://www.netlib.org/go/fft.f
 or look at
  http://theory.lcs.mit.edu/~fftw/fft-links.html
  http://theory.lcs.mit.edu/~fftw
  http://www.spektracom.de/~arndt/fxt/fxtpage.html

in order to use that, you must have data over a full period 
(minus the last point). these data
are then interpolated by a finite fourier series. the backward process 
gives you the values for a finite fourier series given by its
coefficients on an equidistant grid of points. in principle this could be done by
writing down a linear system of equations. the clue is the efficiency of
fft, which goes from O(n**3) down to O(n log n) n=number of data. 
hope this helps
peter