Abstract
The object of this chapter is to briefly summarize the main properties of the discrete Fourier transform (DFT) and to present various fast DFT computation techniques known collectively as the fast Fourier transform (FFT) algorithm. The DFT plays a key role in physics because it can be used as a mathematical tool to describe the relationship between the time domain and frequency domain representation of discrete signals. The use of DFT analysis methods has increased dramatically since the introduction of the FFT in 1965 because the FFT algorithm decreases by several orders of magnitude the number of arithmetic operations required for DFT computations. It has thereby provided a practical solution to many problems that otherwise would have been intractable.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. Gold, C. M. Rader: Digital Processing of Signals (McGraw-Hill, New York 1969)
E. O. Brigham: The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N. J. 1974)
L. R. Rabiner, B. Gold: Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N. J. 1975)
A. V. Oppenheim, R. W. Schafer: Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N. J. 1975)
A. E. Siegman: How to compute two complex even Fourier transforms with one transform step. Proc. IEEE 63, 544 (1975)
J. W. Cooley, J. W. Tukey: An algorithm for machine computation of complex Fourier series. Math. Comput. 19, 297–301 (1965)
G. D. Bergland: A fast Fourier transform algorithm using base 8 iterations. Math. Comput. 22, 275–279 (1968)
R. C. Singleton: An algorithm for computing the mixed radix fast Fourier transform. IEEE Trans. AU-17, 93–103 (1969)
R. P. Polivka, S. Pakin: APL: the Language and Its Usage (Prentice-Hall, Englewood Cliffs, N. J. 1975)
P. D. Welch: A fixed-point fast Fourier transform error analysis. IEEE Trans. AU-17, 151–157 (1969)
T. K. Kaneko, B. Liu: Accumulation of round-off errors in fast Fourier transforms. J. Assoc. Comput. Mach. 17, 637–654 (1970)
C. J. Weinstein: Roundoff noise in floating point fast Fourier transform computation. IEEE Trans. AU-17, 209–215 (1969)
C. M. Rader, N. M. Brenner: A new principle for fast Fourier transformation. IEEE Trans. ASSP-24, 264–265 (1976)
S. Winograd: On computing the discrete Fourier transform. Math. comput. 32, 175–199 (1978)
K. M. Cho, G. C. Ternes: “Real-factor FFT algorithms”, in IEEE 1978 Intern. Conf. Acoust., Speech. Signal Processing. pp. 634–637
H. J. Nussbaumer, P. Quandalle: Fast computation of discrete Fourier transforms using polynomial transforms. IEEE Trans. ASSP-27. 169–181 (1979)
G. Bonnerot, M. Bellanger: Odd-time odd-frequency discrete Fourier transform for symmetric real-valued series. Proc. IEEE 64, 392–393 (1976)
G. Bruun: z-transform DFT filters and FFTs. IEEE Trans. ASSP-26, 56–63 (1978)
G. K. McAuliffe: “Fourier Digital Filter or Equalizer and Method of Operation Therefore”, US Patent No. 3 679 882, July 25, 1972
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Nussbaumer, H.J. (1981). The Fast Fourier Transform. In: Fast Fourier Transform and Convolution Algorithms. Springer Series in Information Sciences, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00551-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-00551-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-00553-8
Online ISBN: 978-3-662-00551-4
eBook Packages: Springer Book Archive