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Multiplicative Characters and the FT

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Algorithms for Discrete Fourier Transform and Convolution

Part of the book series: Signal Processing and Digital Filtering ((SIGNAL PROCESS))

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Abstract

Fix an odd prime p throughout this chapter. For m > 1, consider the subspace

$$ L\left( {p,p^{m - 1} } \right)\, \subset L\left( {Z/p^m } \right) $$

.

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References

  1. Tolimieri, R. “Multiplicative Characters and the Discrete Fourier Transform”, Adv. in Appl. Math., 7, 1986, pp. 344–380.

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  2. Auslander, L., Feig, E. and Winograd, S. “The Multiplicative Complexity of the Discrete Fourier Transform”, Adv. in Appl. Math., 5, 1984, pp. 31–55.

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  3. Rader, C. “Discrete Fourier Transforms When the Number of Data Samples is Prime”, Proc. IEEE, 56, 1968, pp. 1107–1108.

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  4. Winograd, S. Arithmetic Complexity of Computations, CBMS Regional Conf. Ser. in Math., Vol. 33, Soc. Indus. Appl. Math., Philadelphia, 1980.

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  5. Tolimieri, R. “The Construction of Orthogonal Basis Diagonalizing the Discrete Fourier Transform”, Adv. in Appl. Math., 5, 1984, pp. 56–86.

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Authors and Affiliations

  1. Department of Electrical Engineering, City College of CUNY, New York, NY, 10037, USA

    Richard Tolimieri

  2. Department of Computer and Information Sciences, Towson State University, Towson, MD, 21204, USA

    Chao Lu

  3. A.J. Devaney Associates, 52 Ashford Street, Allston, MA, 02134, USA

    Myoung An

Authors
  1. Richard Tolimieri
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  2. Chao Lu
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  3. Myoung An
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© 1997 Springer Science+Business Media New York

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Tolimieri, R., Lu, C., An, M. (1997). Multiplicative Characters and the FT. In: Algorithms for Discrete Fourier Transform and Convolution. Signal Processing and Digital Filtering. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2767-8_14

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  • DOI: https://doi.org/10.1007/978-1-4757-2767-8_14

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-3115-3

  • Online ISBN: 978-1-4757-2767-8

  • eBook Packages: Springer Book Archive

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