HP 48g Graphing Calculator - Manual (Page 163)

Fast Fourier Transforms
A physical process can be described in two distinct ways:
■ The change of a quantity, h, as a function of time, i (k(t)).
m
The change of an amplitude, II, as a function of frequency, /
For many situations, it helps to consider h(t) and H(f) as two different
representations of the same function. Fourier transforms are used to
switch between these representations, or domains.
The HP 48 can perform discrete Fourier transforms, whereby a
sequence of discretely sampled data can be transformed into the
“other” domain. The HP 48 performs “Fast” Fourier transforms,
which make use of computational efficiencies that require that the
number of rows and the number of columns in the sample set to be a
integral power of 2.
Fast Fourier transforms are most commonly used in analyzing
one-dimensional signals or two-dimensional images. The HP 48
commands can handle both cases. In the first case the data should be
entered as a vector of N elements where N is an integral power of 2 (2,
4, 8, 16, 32, ... ). In the second case, the data should be entered as
a matrix of M rows by N columns where both M and N are integral
powers of 2.
The “forward” transformation (FFT) maps an array of MxN real or
complex numbers (hk) in the time domain to an array of MxN real or
complex numbers (Hn) in the frequency domain:
N - l
13
Hk =
- ^ n i k n l N
The “inverse” transformation (IFFT) maps an array of MxN real or
complex numbers (Hn) in the frequency domain to an array of MxN
real or complex numbers (hk) in the time domain:
2 ^ __^
N - l
2 T r i k n f N
k = 0
Vectors and Transforms 13-7