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

Chapter 5 Fast Fourier Transforms 541
One-dimensional FFT Subprograms for Fast Fourier Transforms
Subprograms for Fast Fourier Transforms
The following sections describe FFT subprograms included with VECLIB.
Name C1DFFT/Z1DFFT
One-dimensional FFT
Purpose Given an array of complex data, these subprograms compute the
one-dimensional forward or inverse DFT. Two companion subprograms,
S1DFFT and D1DFFT, perform the same operation but with the complex data
presented with real and imaginary parts in separate real arrays.
The one-dimensional forward DFT of z(n), for n = 1, 2, ..., l, is defined by
for m = 1, 2, ..., l and .
Alternatively, the one-dimensional scaled inverse DFT of Z(m), for
m = 1, 2, ..., l, is defined by
for n = 1, 2, ..., l.
Finally, the one-dimensional unscaled inverse DFT of Z(m), for m = 1, 2, ..., l,
is defined by
for n = 1, 2, ..., l.
For best performance, these subprograms require that l be a product of powers
of 2, 3, and 5, that is, of the form
l =2
p
3
q
5
r
where p, q, r ≥ 0
Zm() zn()e
2– πim 1–()n 1–()l⁄
n 1=
l
∑
=
i 1–=
zn()
1
l
---
Zm()e
+2πim 1–()n 1–()l⁄
m 1=
l
∑
=
zn() Zm()e
+2πim 1–()n 1–()l⁄
m 1=
l
∑
=