In mathematics the finite Fourier transform may refer to either
- another name for the discrete Fourier transform
or
- another name for the Fourier series coefficients
or
- a transform based on a Fourier-transform-like integral applied to a function, but with integration only on a finite interval, usually taken to be the interval . Equivalently, it is the Fourier transform of a function multiplied by a rectangular window function. That is, the finite Fourier transform of a function on the finite interval is given by:
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