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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