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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
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a comple ...
(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
The short-time Fourier transform (STFT), is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divi ...
.[
]
See also
* Fourier transform
Notes
References
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#
Further reading
*Rabiner, Lawrence R.; Gold, Bernard (1975). ''Theory and application of digital signal processing''. Englewood Cliffs, N.J.: Prentice-Hall. pp 65–67. .
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Transforms
Fourier analysis
Fourier series