Fast Fourier transform

Syntax: m = FFT(y)
m = FFT(y,'AMP&PHASE')
m = FFT(y,'COS&SIN')

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