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Fast DFT Matrices Transform Based on Generalized Prime Factor Algorithm  

Guo, Ying (School of Information Science and Engineering, Central South University)
Mao, Yun (School of Information Science and Engineering, Central South University)
Park, Dong-Sun (Electronics and Information Engineering, Chonbuk National University)
Lee, Moon-Ho (Electronics and Information Engineering, Chonbuk National University)
Publication Information
Journal of Communications and Networks / v.13, no.5, 2011 , pp. 449-455 More about this Journal
Abstract
Inspired by fast Jacket transforms, we propose simple factorization and construction algorithms for the M-dimensional discrete Fourier transform (DFT) matrices underlying generalized Chinese remainder theorem (CRT) index mappings. Based on successive coprime-order DFT matrices with respect to the CRT with recursive relations, the proposed algorithms are presented with simplicity and clarity on the basis of the yielded sparse matrices. The results indicate that our algorithms compare favorably with the direct-computation approach.
Keywords
Discrete Fourier transform (DFT) matrices; fast Jacket transform; generalized prime factor algorithm (GPFA); Kronecker product; sparse matrices;
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1 W. Song, M. H. Lee, and G. Zeng, "Orthogonal space-time block codes design using Jacket transform for MIMO transmission system," in Proc. IEEE ICC, May 2008, pp. 766-769.
2 S. Winograd, "On computing the discrete Fourier transform," in Proc. Nat. Acad. Sci., USA, vol. 73, no. 4, Apr. 1976, pp. 1005-1006.
3 C. Temperton, "Implementation of a self-sorting, in-place prime factor FFT algorithm," J. Computat. Physics, vol. 58, pp. 283-299, 1985.   DOI
4 C. S. Burrus, "Index mapping for multidimensional formulation of the DFT and convolution," IEEE Trans. Acoust. Speech, Signal Process., vol. 25, no. 3, pp. 239-242, June 1977.   DOI
5 C. S. Burrus and P. W. Eschenbacher, "An in-place, in-order prime factor for FFT algorithm," IEEE Trans. Acoust. Speech, Signal Process., vol. 29, no. 4, pp. 806-817, Aug. 1981.   DOI
6 Z. Wang, "Index mapping for one to multidimensional," Electron. Lett., vol. 25, no. 12, pp. 781-782, June 1989.   DOI   ScienceOn
7 J. C. Schatzman, "Index mapping for the fast Fourier transform," IEEE Trans. Signal Process., vol. 44, no. 3, pp. 717-719, Mar. 1996.   DOI   ScienceOn
8 H. Neudecker, "A note on Kronecker matrix products and matrix equation systems," SIAM J. Appl. Mathematics, vol. 17, no. 3, pp. 603-606, May 1969.   DOI   ScienceOn
9 R. A. Horn and C. R. Johnson, Topics in Matrix Analysis. New York: Cambridge Univ. Press, 1991.
10 N. Ahmed and K. R. Rao, Orthogonal Transform for Digital Signal Processing. Berlin, Germany: Springer Verlag, 1975.
11 R. E. Blahut, Algebraic Codes for Data Transmission. Cambridge, UK: 2003.
12 K. Y. Rao and J. E. Hershey, Hadamard Matrix Analysis and Synthesis. Norwell, MA: Kluwer, 1997.
13 M. H. Lee, "The center weighted Hadamard transform," IEEE Trans. Circuits Syst., vol. 36, pp. 1247-1249, Sept. 1989.   DOI   ScienceOn
14 M. H. Lee, "A new reverse Jacket transform and its fast algorithm," IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process, vol. 47, no. 1, pp.39-47, Jan. 2000.   DOI   ScienceOn
15 M. H. Lee and Y. L. Borissov, "A proof of non-existence of bordered Jacket matrices of odd order over some field," Electron. Lett., vol. 46, pp. 349-351, Mar. 2010.   DOI   ScienceOn
16 M. H. Lee, B. S. Rajan, and J. Y. Park, "A generalized reverse Jacket transform," IEEE Trans. Circuits Syst., vol. 48, pp. 684-688, July 2001.   DOI   ScienceOn
17 M. H. Lee and J. Hou, "Fast block inverse Jacket transform," IEEE Signal Process. Lett., vol. 13, no. 4, pp. 461-464, 2006.   DOI
18 M. H. Lee and G. Zeng, "Family of fast Jacket transform algorithms," Electron. Lett., vol. 43, no. 11, pp. 651-651, 2007.   DOI   ScienceOn
19 G. Zeng and M. H. Lee, "A generalized reverse block Jacket transform," IEEE Trans. Circuits and Syst., vol. 55, pp. 1589-1599, July 2008.   DOI
20 Z. Chen, M. H. Lee, and G. Zeng, "Fast cocyclic Jacket transform," IEEE Trans. Signal Process., vol. 56, no. 5, pp. 2143-2148, 2008.   DOI
21 M. H. Lee and K. Finlayson, "A simple element inverse Jacket transform coding," in Proc. IEEE ITW, New Zealand, vol. 14, 2006, pp. 1-4.
22 X. J. Jiang and M. H. Lee, "Higher dimensional Jacket code for mobile communications," in Proc. APW, Sapporo, Japan, Aug. 2005, pp. 4-5.
23 M. G. Parker and M. H. Lee, "Optimal bipolar sequence for the complex reverse-Jacket transform," in Proc. ISITA, Honolulu, USA, Nov. 2000, pp.5-8.
24 J. Hou and M. H. Lee, Cocyclic Jacket Matrices and Its Application to Cryptography Systems. Berlin, Germany: Springer, vol. 3391, 2005.