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DCL:MATH2:FFTLIB: Fast Fourier Transformation: Explanation of Subroutines

2.3.2 EZFFTI/EZFFTF/EZFFTB

1.

Function

A simplified subroutine group of RFFTI, RFFTF, and RFFTB: EZFFTI initializes; EZFFTF performs forward Fourier transformation; and EZFFTB performs inverse Fourier transformation.

2.

Definition

Forward transformation is defined as follows: (When N is even, N'' = N/2-1, and when N is odd, N'' = (N-1)/2.)

However, note that when N is even,

Inverse transformation is defined as follows: (When N is even, N'' = N/2, and when N is odd, N'' =(N-1)/2.)

$$R_{i} = a_{0} + \sum_{k=1}^{N'}( a_{k} \cos \frac{2\pi (i-1......c{2\pi (i-1)k}{N})\mbox{\hspace{1em}}( i = 1, \ldots, N ).$$

3.

Call

CALL EZFFTI(N,WSAVE)
CALL EZFFTF(N,R,A0,A,B,WSAVE)
CALL EZFFTB(N,R,A0,A,B,WSAVE)

4.

Explanation of Parameters

N	(I)	Length of data to process.
WSAVE	(R)	Working array: must have a length of at least 3 N+15.
R	(R)	Floating-point array to process. It is the input parameter for EZFFTF, and the output parameter for EZFFTB.
A0	(R)	A0 and a0 in above definition.
A, B	(R)	A floating-point array with length of N/2 when N is even, and (N-1)/2 when N is odd. (See above definition.)

5.

Note

(a)

This transformation performs normalization. In other words, when EZFFTF and EZFFTB are called successively, then the original value is returned.