HP MLIB User's Guide Vol. 2 7th Ed.

556 HP MLIB User’s Guide

CFFTS/ZFFTS Simultaneous one-dimensional FFT

Name CFFTS/ZFFTS

Simultaneous one-dimensional FFT

Purpose Given a number of sets of one-dimensional complex data in a complex array,

these subprograms compute all of their one-dimensional forward or inverse

DFT. Two companion subprograms, SFFTS and DFFTS, perform the same

operation but with the complex data presented with real and imaginary parts

in separate real arrays. Other subprograms, documented elsewhere in this

chapter, are more suited for computing just one transform.

The one-dimensional forward DFT of a complex data set z(n), for

n = 1, 2, ..., l, is deﬁned by

for m = 1, 2, ..., l and .

Alternatively, the one-dimensional scaled inverse DFT of a data set Z(m), for

m = 1, 2, ..., l, is deﬁned by

for n = 1, 2, ..., l.

These subprograms perform forward or inverse transform operations

simultaneously on a number of data sets. For best performance, they require

that the length l of the data sets be a product of powers of 2, 3, and 5, that is, of

the form

where p, q, r ≥ 0.

Usage VECLIB:

INTEGER*4 l, incl, n, incn, iopt, ier

COMPLEX*8 z(lenz)

CALL CFFTS(z, l, incl, n, incn, iopt, ier)

INTEGER*4 l, incl, n, incn, iopt, ier

COMPLEX*16 z(lenz)

CALL ZFFTS(z, l, incl, n, incn, iopt, ier)

Zm() zn()e

2– πim 1–()n 1–()l⁄

n 1=

∑

i 1–=

zn()

---

Zm(()e

+2πim 1–()n 1–()l⁄

m 1=

∑

l 2