Fast Fourier transform
Syntax: |
m = FFT(y)
|
The FFT
function calculates the
discrete fast Fourier transform of the input variable,
y
. By default, FFT
returns the amplitudes and
the phases, where the phases are in degrees. If the
COS&SIN
keyword is used, FFT
returns the Fourier
coefficients.
Note that the reason that the amplitudes and phases are returned by default is historical. Actually, the Fourier coefficients, that is, the cosine and sine coefficients, are calculated and the amplitudes and phases are just derived from them, as described below. It is a simple matter for the user to request the cosine and sine coefficients, and then to calculate the amplitudes and phases him/herself.
Suppose that the length of the input vector is 2N
. The
output of this function is a matrix with N+1
rows and 2
columns. The first column contains the amplitudes (or the cosine
coefficients), and the second column contains the phases (or the sine
coefficients).
The IFFT
function
calculates the inverse fast Fourier transform.
Fourier coefficients
Discrete Fourier series
Restrictions
Prime factors
Example