The following two requirements are satisfied in the FFT subroutine. 



(a) By operating on the sampled function, obtaining the F(n) 

 coefficients and carrying out the inverse FFT (FFT -1 ), the original 

 time function is recovered. Schematically, 



f(j) + FFT + F(n) + FFT -1 * f ( j ) * 



(b) The mean square of the sampled time function is equal to the 

 sum of the squares of the moduli of the FFT coefficients, F(n) , i.e., 



j N N-l 



- I [f(j)] 2 = I |F(n)|2 



N j=l n=o 



a. Calling Statement : SUBROUTINE FFT (FR, FI, K, ICO) (see Fig. 3). FR, 

 FI = real and imaginary coefficients in 



F(n) = FR(n) - iFI(n) 



K = power of two (i.e., N = 2"^) 



>K> 



ICO = control whether FFT or (FFT) 1 



operation is desired if 



ICO 



= ->- FFT 



= 1 ■* (FFT) -1 



When entering the subroutine, FR is the time sequence f(j) and FI is 

 arbitrary. When exiting the subroutine, FR and FI are the real and imagi- 

 nary parts of the complex transform, respectively; e.g., input is 



K = 5 



ICO = 



f(j) = 1.0 + 2.0 cos il^+ 3.0 cos *&§Sl 



. , . 2ir(jAt) , . . 4ir(jAt) 

 - 0.6 sin — ^ — '- - 1.4 sin — ^ — '- 



24 



