Practical signal processing is based on the fast Fourier transform (FFT), an efficient algorithm for computing a discrete Fourier transform (DFT). While the FFT has a speed advantage, it is limited to data record lengths that are powers of 2. The slower DFT can operate on data records of any length. Except for the restriction on an FFT, FFT and DFT are interchangeable.
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References
A. Oppenheim and R. Schafer, Discrete-Time Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, 1989.
R. Bracewell, The Fast Fourier Transform and Its Applications, 2nd Ed., Rev. McGraw-Hill Book Company, New York, NY, 1986.
J. C. Burgess, “Practical considerations in signal processing”, in Encyclopedia of Acoustics (M. Crocker, ed.), vol. 3, ch. 101, pp. 1261–1279. Wiley, New York, 1997.
J. C. Burgess, “Chirp design for acoustical system identification”, J. Acoust. Soc. Am., vol. 91, pp. 1525–1530, 1992.
J. Proakis and D. Manolakis, Introduction to Digital Signal Processing. Macmillan, New York, 1988.
G. Jenkins and D. Watts, Spectral Analysis and Its Applications. Holden-Day, San Francisco, 1969.
F. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform”, Proc. IEEE, vol. 66, pp. 51–83, 1978.
C. Dolph, “A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level”, Proc. I.R.E, vol. 34, pp. 335–348, June 1946.
H. Helms, “Nonrecursive digital filters: design methods for achieving specifications on frequency response”, IEEE Trans. Audio Electroacoust., vol. AU-16, pp. 336–342, 1968.
R. A. Roberts and C. T. Mullis, Digital Signal Processing. Addison-Wesley, Reading, MA, 1987.
L. Rabiner, B. Gold, and C. McGonegal, “An approach to the approximation problem for nonrecursive digital filters”, IEEE Trans. Audio Electroacoust., vol. AU-18, pp. 83–106, 1970.
J. C. Burgess, “Optimum approximations to Dolph–Chebyshev data windows”, IEEE Trans. Signal Process, vol. 40, no. 10, pp. 2592–2594, 1992.
A. Nuttall, “Some windows with very good sidelobe behavior”, IEEE Trans. Acoust., Speech Signal Process, vol. ASSP-29, pp. 84–91, 1981.
J. C. Burgess, “Accurate analysis of multitone signals using a DFT”, J. Acoust. Soc. Am., vol. 116, pp. 369–395, 2004.
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Burgess, J.C. (2008). The FFT and Tone Identification. In: Havelock, D., Kuwano, S., Vorländer, M. (eds) Handbook of Signal Processing in Acoustics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30441-0_4
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