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

544 HP MLIB User’s Guide
S1DFFT/D1DFFT One-dimensional FFT
Name S1DFFT/D1DFFT
One-dimensional FFT
Purpose Given a set of complex data with the real and imaginary parts in separate real
arrays, these subprograms compute the one-dimensional forward or inverse
DFT. Two companion subprograms, C1DFFT and Z1DFFT, perform the same
operation but with the complex data presented in a complex array.
The one-dimensional forward discrete Fourier transform 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 power of
2, 3 and 5, that is, of the form
l =2
p
3
q
5
r
with p, q, r ≥ 0
The complex data, z or Z, are stored with real and imaginary parts in separate
real arrays, x and y, respectively.
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
∑
=