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

2.3.3 SINTI/SINT

1.

Function

Performs sine transformation on odd cyclic data: SINTI initializes; and SINT performs sine transformation.

2.

Definition

Forward transformation is defined as follows:

$$X_{k} = 2\sum_{i=1}^{N}x_{i}\sin \frac{\pi ik}{N+1},\mbox{\hspace{1em}}( k = 1, \ldots, N ).$$

Inverse transformation is the same as the forward transformation.

3.

Call

CALL SINTI(N,WSAVE)
CALL SINT(N,R,WSAVE)

4.

Explanation of Parameters

N	(I)	Length of data to process
WSAVE	(R)	Working array. Must have a length of at least 2.5 N+15.
R	(R)	Floating-point array to process. It is both the input and output parameter. (See above definition.)

5.

Note

(a)

SINT is also the inverse transformation. This transformation does not involve normalization. In other words, if SINT is called twice, then the value of the original value multiplied by a factor of 2(N+1) is returned.