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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 821949, 9 pages
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.
- H. Bruns, Grundlinien des Wissenschaftlichichnen Rechnens, B. G. Teubner, Leipzig, Germany, 1903.
- A. Wintner, An Arithmetical Approach to Ordinary Fourier Series, Waverly Press, Baltimore, Md, USA, 1946.
- G. Sadasiv, “The arithmetic Fourier transform,” IEEE ASSP Magazine, vol. 5, no. 1, pp. 13–17, 1988.
- 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.
- 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.
- L. Knockaert, “Generalized Mobius transform and arithmetic fourier transforms,” IEEE Transactions on Signal Processing, vol. 42, no. 11, pp. 2967–2971, 1994.
- 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.
- 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.
- 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.
- T. M. Apostol, Introduction to Analytic Number Theory, Springer, New York, NY, USA, 1976.