D705: Real Fast Fourier Transform

Author(s): K.S. Kölbig, H.-H. Umstätter	Library: MATHLIB
Submitter:	Submitted: 22.04.1996
Language: Fortran	Revised:

Subroutine RFSTFT calculates the finite Fourier transform of a real periodic sequence , whose period n must be a power of two. Either the direct transform

or the inverse transform

where are real and are complex numbers, may be calculated. Note that , where denotes the complex conjugate of . Thus, only the numbers for which are calculated.

Structure:

SUBROUTINE subprogram
User Entry Names: RFSTFT
External References: CFSTFT

Usage:

    COMPLEX C(0:..)
    REAL Y(0:..)
    EQUIVALENCE (C,Y)
    ...
    CALL RFSTFT(M,C)
    ...

M

(INTEGER) On entry, n is determined by the absolute value of M via .
The direct transform (1) is calculated.
The inverse transform (2) is calculated.
Unchanged on exit.

C

(COMPLEX) One dimensional array of dimension (0:d), where .

Y

(REAL) One dimensional array of dimension (0:d), where .

On entry, .
On exit, , as defined by (1).

On entry, .
On exit, , as defined by (2).

Method:

The subroutine uses CFSTFT (D705) with sequences reduced to half of their length as explaind in Ref. 1.

References:

1. E.O. Brigham, The fast Fourier transform, (Prentice-Hall, Englewood Cliffs, 1974) Ch. 10, Sect. 10, Fig. 10-10.