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.Template:Efn-ua 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
Notes
References
- ↑ 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).
Further reading
- Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, N.J.: Prentice-Hall. pp 65–67. Template:ISBN.