Finite Fourier transform

In mathematics the finite Fourier transform may refer to either

• another name for discrete-time Fourier transform (DTFT) of a finite-length series.  E.g., F.J.Harris (pp. 52–53) describes the finite Fourier transform as a "continuous periodic function" and the discrete Fourier transform (DFT) as "a set of samples of the finite Fourier transform".  In actual implementation, that is not two separate steps; the DFT replaces the DTFT.  So J.Cooley (pp. 77–78) describes the implementation as discrete finite Fourier transform.

or

• another name for the Fourier series coefficients.

or

• another name for one snapshot of a short-time Fourier transform.