DEFINITION MODULE FFTs;

   (* EXPORT QUALIFIED CosFT, RealFT, SinFT, TwoFFT; *)

   FROM NRVect IMPORT Vector;

   PROCEDURE CosFT(Y: Vector; isign: INTEGER); 
   (*
     Calculates the cosine transform of a set y[0, n-1] of real-valued
     data points. The transformed data replace the original data in array
     y. n must be a power of 2. Set isign to +1 for a transform,
     and to -1 for an inverse transform. For an inverse transform, the output
     array should be multiplied by 2/n.
   *)

   PROCEDURE RealFT(DATA:  Vector; n:  INTEGER; isign: INTEGER); 
   (*
     Calculates the Fourier Transform of a set of 2n real-valued data
     points. Replaces this data (which is stored in array DATA[0, 2n-1]) by the
     positive frequency half of its complex Fourier Transform. The real-valued 
     first and last components of the complex transform are returned as elements 
     DATA[0] and DATA[1] respectively. n must be a power of 2. This routine
     also calculates the inverse transform of a complex data array if it is the
     transform of real data. (Result in this case must be multiplied by 1/n.)
   *)

   PROCEDURE SinFT(Y: Vector); 
   (*
     Calculates the sine transform of a set of n real-valued data
     points stored in array y[0, n-1]. The number n must be a power of 2. 
     On exit y is replaced by its transform. This program, without changes, also
     calculates the inverse sine transform, but in this case the output array
     should be multiplied by 2/n.
   *)

   PROCEDURE TwoFFT(DATA1, DATA2, FFT1, FFT2: Vector; n: INTEGER); 
   (*
     Given two real input arrays DATA1[0, n-1] and DATA2[0, n-1],
     this routine calls Four1 and returns two complex output arrays, 
     FFT1 and FFT2, each of complex length n (i.e.real dimensions [0, 2n-1]), 
     which contain the discrete Fourier transforms of the respective DATAs. 
     n MUST be an integer power of 2.
   *)

END FFTs.