About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 821949, 9 pages
http://dx.doi.org/10.1155/2012/821949
Research Article

Dirichlet Characters, Gauss Sums, and Inverse Z Transform

1Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an, Shaanxi, China
2Department of Mathematics, Northwest University, Xi'an, Shaanxi, China

Received 26 December 2011; Accepted 9 January 2012

Academic Editor: Karl Joachim Wirths

Copyright © 2012 Jing Gao and Huaning Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Bruns, Grundlinien des Wissenschaftlichichnen Rechnens, B. G. Teubner, Leipzig, Germany, 1903.
  2. A. Wintner, An Arithmetical Approach to Ordinary Fourier Series, Waverly Press, Baltimore, Md, USA, 1946.
  3. G. Sadasiv, “The arithmetic Fourier transform,” IEEE ASSP Magazine, vol. 5, no. 1, pp. 13–17, 1988. View at Publisher · View at Google Scholar · View at Scopus
  4. I. S. Reed, D. W. Tufts, X. Yu, T. K. Truong, M. T. Shih, and X. Yin, “Fourier analysis and signal processing by use of the Mobius inversion formula,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, no. 3, pp. 458–470, 1990. View at Publisher · View at Google Scholar · View at Scopus
  5. I. S. Reed, M. T. Shih, T. K. Truong, E. Hendon, and D. W. Tufts, “A VLSI architecture for simplified arithmetic Fourier transform algorithm,” IEEE Transactions on Signal Processing, vol. 40, no. 5, pp. 1122–1133, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. L. Knockaert, “Generalized Mobius transform and arithmetic fourier transforms,” IEEE Transactions on Signal Processing, vol. 42, no. 11, pp. 2967–2971, 1994. View at Publisher · View at Google Scholar · View at Scopus
  7. L. Knockaert, “A generalized möbius transform, arithmetic fourier transforms, and primitive roots,” IEEE Transactions on Signal Processing, vol. 44, no. 5, pp. 1307–1310, 1996. View at Publisher · View at Google Scholar · View at Scopus
  8. J. L. Schiff, T. J. Surendonk, and W. J. Walker, “An algorithm for computing the inverse Z transform,” IEEE Transactions on Signal Processing, vol. 40, no. 9, pp. 2194–2198, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. C. C. Hsu, I. S. Reed, and T. K. Truong, “Inverse Z-transform by Mobius inversion and the error bounds of aliasing in sampling,” IEEE Transactions on Signal Processing, vol. 42, no. 10, pp. 2823–2830, 1994. View at Publisher · View at Google Scholar · View at Scopus
  10. T. M. Apostol, Introduction to Analytic Number Theory, Springer, New York, NY, USA, 1976. View at Zentralblatt MATH