
  Arbitrary Length FFT
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  NOTE : This is copyrighted material, NOT public domain. See below.
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  Contents:
      This packet contains the C source for a mixed-radix FFT routine. 
      It performs a fast discrete Fourier transform (FFT) of a complex 
      sequence, x, of an arbitrary length, n. The output, y, is also a 
      complex sequence of length n.

      y[k] = sum(x[m]*exp(-i*2*pi*k*m/n), m=0..(n-1)), k=0,...,(n-1)

      The largest prime factor of n must be less than or equal to the
      constant, maxPrimeFactor defined in mixfft.c. The input/output 
      variables are each stored in two arrays comprising the real part
      and the imaginary part respectively. 
 
      The routine is accompanied by a demo program, fftbench.c,  that 
      demonstrates the numerical capabilities. It measures the execution 
      time as well. If you wish to test the capabilities of another FFT
      routine, the fftbench.c is easy to modify.
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  Filelist:
      mixfft.c      21.120 001030  The C source for the mixed-radix FFT.
      fftbench.c     8.724 001030  The C source for FFT benchmark program.
      fftbench.exe  62.976 001030  The PC executable.
      readme.txt                   This file.
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  Platforms:
  
  PC:
      The included fftbench.exe was generated using the Microsoft Visual 
      C++ compiler with the following compile options:
      /nologo /Gs /G2 /W4 /AH /Ox /D "NDEBUG" /D "_DOS" /FR
      It was tested on a 50MHz 486DX. Please refer to fftbench.c for some
      benchmarks. (jjn, March 1996)
      
  Other:
      Your experience with other platforms are warmly welcomed. Please
      e-mail me.
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  Conditions:
      The source code in this packet is copyrighted material.
      
      Non-commercial use of the source code is free.
      
      A $100 fee must be paid if used commercially. Please contact me at
      jjn@get2net.dk and register your copy. The $100 fee includes 
      up to one hour of assistance related to your use of the code. A 
      trial period of 14 days is allowed. 

      If the code is used for professional (paid) research and development 
      for non-profit organisations like universities a reduced fee of $20
      must be paid.
      
      The commercial license allows you to include the compiled code in a
      product or to use the code on a regular basis. You are however NOT
      allowed to sell the source code.        
      
      Distribution of the complete unaltered package, including this
      file, is free. This includes commercial CD's.
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  Author:
      Jens Joergen Nielsen            For non-commercial use only.
      Bakkehusene 54                  A $100 fee must be paid if used
      2970 Hoersholm                  commercially. Please contact.
      DENMARK

      mailto:jjn@get2net.dk   All rights reserved. October 2000.

      Check my homepage for updates and FAQ's http://home.get2net.dk/jjn
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  Release notes:
      V.0.1 950301      Initial MIXFFT release.
      V.0.3 960317      Input/output variables have separate arrays for
                        real and imag part. The speed of prime factors
                        larger than 7 is more than doubled.
      V.0.4 980103      e-mail address changed.
      V.0.5 001030      Memory allocation in FFTBench changed, now calloc
                        is used. Error reporting when primefactor is 
                        larger than maxPrimeFactor has been corrected.

      
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