FFT.PAS is an implementation of the radix-2, fast Fourier trans-
form algorithm with decimation in time (Cooley-Tukey method).  This
program is essentially the same as that found in J.W. Cooper, "Intro-
duction to Pascal for Scientists," (Wiley:1981) pp. 211-216.  I do
not particularly recommend this book in general, but the FFT program
is solid and in the author's area of expertise.  Also, variable names
and program structure follow closely to the discussion in the text.
There were, however, several blunders in Cooper's post-processing pro-
cedure which I have corrected.  Furthermore, I incorporated more effi-
cient code in a number of places (for example, the required sines and
cosines are computed recursively using only the SQRT function).

     By rearranging the procedure calls in the main body, you can
perform other calculations.  Some common usages are:


          Forward Transform    ----->  FFT(FORWRD);
            Complex Vector

          Inverse Transform    ----->  FFT(INVERSE);
            Complex Vector

          Inverse Transform    ----->  POST_PROCESS(INVERSE);
             Real Vector               FFT(INVERSE);
                                       SHUFFLE(INVERSE);


     There are many methods of computing discrete Fourier transforms
in order (N log N) floating point operations.  The differences can
usually be attributed to various ways the data are accessed or to
the optimal computational structure as dictated by the available
hardware.  FFT.PAS represents an efficient, but relatively straight-
forward approach well suited to microprocessors.

     For those interested in studying FFT's further, I suggest:


           J.D. Lipson, "Elements of Algebra and Algebraic
              Computing," (Addison-Wesley:1981).

           H. Nussbaumer, "Fast Fourier Transform and Convolution
              Algorithms," (Springer-Verlag:1982).

           E.O. Brigham, "The Fast Fourier Transform," (Prentice-
              Hall:1974).