Finite Fourier transform
In mathematics the finite Fourier transform may refer to either
- shorthand version of "discrete finite Fourier transform". (J. Cooley et al, p 77, par 2)
or
- another name for the discrete Fourier transform (DFT). I.e., J. Cooley et al, p 78, gives a mathematical formula that is identical to the DFT, except for a scale factor.
or
- another name for discrete-time Fourier transform (DTFT) of a finite-length series. I.e., F.J. Harris, p 52, describes the finite Fourier transform as a "continuous periodic function" and the DFT as "a set of samples of the 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]
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).
- Harris, Fredric J. (Jan 1978). "On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform" (PDF). Proceedings of the IEEE. 66 (1): 51–83. doi:10.1109/PROC.1978.10837.
- Cooley, J.; Lewis, P.; Welch, P. (1969). "The finite Fourier transform" (PDF). IEEE Trans. Audio Electroacoustics. 17 (2): 77–85.
Further reading
- Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, N.J.: Prentice-Hall. pp 65–67. ISBN 0139141014.
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