Finite Fourier transform
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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 (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.[A] So J.Cooley (pp. 77–78) describes the implementation as discrete finite Fourier transform.
or
- another name for the Fourier series coefficients.[1]
or
- another name for one snapshot of a short-time Fourier transform.[2]
See also
[edit | edit source]Notes
[edit | edit source]- ^ Harris' motivation for the distinction is to distinguish between an odd-length data sequence with the indices which he calls the finite Fourier transform data window, and a sequence on which is the DFT data window.
References
[edit | edit source]- ^ George Bachman, Lawrence Narici, and Edward Beckenstein, Fourier and Wavelet Analysis (Springer, 2004), p. 264
- ^ Morelli, E., "High accuracy evaluation of the finite Fourier transform using sampled data," NASA technical report TME110340 (1997).
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Further reading
[edit | edit source]- Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, N.J.: Prentice-Hall. pp 65–67. Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value)..