public class FFT extends Object implements Serializable, Cloneable
Class FFT
computes the discrete Fourier transform of a real
vector of size n. The method used is a variant of the
CooleyTukey algorithm, which is most efficient when n
is a product of small prime factors. If n satisfies
this condition, then the computational effort is proportional to
n log n.
The forward
method computes the forward transform. If
n is even, then the forward transform is
If n is odd, is defined as above for m from 1 to (n  1)/2.
Let f be a real valued function of time. Suppose we sample f at n equally spaced time intervals of length seconds starting at time . That is, we have
We will assume that n is odd for the remainder of
this discussion. The class FFT
treats this sequence as if
it were periodic of period n. In particular, it
assumes that . Hence, the period of the function is assumed to be
. We can invert the above transform for
p as follows:
This formula is very revealing. It can be interpreted in the following
manner. The coefficients q produced by FFT
determine an interpolating trigonometric polynomial to the data. That is,
if we define
then we have
Now suppose we want to discover the dominant frequencies, forming the vector P of length (n + 1)/2 as follows:
These numbers correspond to the energy in the spectrum of the signal. In particular, corresponds to the energy level at frequency
Furthermore, note that there are only resolvable frequencies when n observations are taken. This is related to the Nyquist phenomenon, which is induced by discrete sampling of a continuous signal. Similar relations hold for the case when n is even.
If the backward
method is used, then the backward transform
is computed. If n
is even, then the backward transform is
If n is odd,
The backward Fourier transform is the unnormalized inverse of the forward Fourier transform.
FFT
is based on the real FFT in FFTPACK, which was
developed by Paul Swarztrauber at the National Center for Atmospheric
Research.
Constructor and Description 

FFT(int n)
Constructs an FFT object.

public FFT(int n)
n
 is the length of the sequence to be transformedpublic double[] backward(double[] coef)
coef
 a double
array containing the Fourier coefficientsdouble
array containing the periodic sequencepublic double[] forward(double[] seq)
seq
 a double
array containing the sequence to be transformeddouble
array containing the transformed sequenceCopyright © 19702015 Rogue Wave Software
Built October 13 2015.