volume | PIER Journals

Abstract

In this paper, a novel version of the transverse wave approach (TWA) based on two-dimensional non-uniform fast Fourier mode transform (2D-NUFFMT) is presented and developed for full-wave analysis of RF integrated circuits (RFICs). An adaptive mesh refinement is applied in this advanced TWA process and CPU computation time is evaluated throughout 30 GHz patch antenna, application belonging to wireless systems. The TWA in its novel version is favorably compared with the conventional one in presence of AMT technique in the context of EM simulations. Another version of TWA is outlined to illustrate a computationally efficient way to handle an arbitrary mesh for RFICs analysis with high complexity problems.

1. Ayari, M., T. Aguili, and H. Baudrand, "More efficiency of Transverse Wave Approach (TWA) by applying Anisotropic Mesh Technique (AMT) for full-wave analysis of microwave planar structures," Progress In Electromagnetics Research B, Vol. 14, 383-405, 2009.
doi:10.2528/PIERB09022001 Google Scholar

2. Ayari, M., T. Aguili, H. Temimi, and H. Baudrand, "An extended version of Transverse Wave Approach (TWA) for full-wave investigation of planar structures," Journal of Microwave, Optoelectronics and Electromagnetic Applications, Vol. 7, No. 2, Dec. 2008. Google Scholar

3. Brigham, E. O., The Fast Fourier Transform, Prentice-Hall, 1974.

4. Dongarra, J. and F. Sullivan, "Introduction to the top 10 algorithms," Computing in Science and Engineering, Vol. 2, No. 1, 2000.
doi:10.1109/MCISE.2000.814652 Google Scholar

5. Cooley, J. W. and J. W. Tukey, "An algorithm for machine calculation of complex fourier series," Math. Computation, Vol. 19, No. 90, 297, 1965.
doi:10.2307/2003354 Google Scholar

6. Sundararajan, D., The Discrete Fourier Transform: Theory, Algorithms and Applications, Prentice-Hall, 2001.

7. Anderson, C. and M. D. Dahleh, "Rapid computation of the discrete Fourier transform," SIAM J. Sci. Comput., Vol. 17, 913-919, 1996.
doi:10.1137/0917059 Google Scholar

8. Oppenheim, A. and D. Johnson, "Computation of spectra with unequal resolution using the fast Fourier transform," Proc. IEEE, Vol. 59, 299-301, Feb. 1971.
doi:10.1109/PROC.1971.8146 Google Scholar

9. Bagchi, S. and S. Mitra, The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing, Kluwer, 1999.

10. Bagchi, S. and S. K. Mitra, "The nonuniform discrete Fourier transform and its applications in filter design. 1 --- 1-D," IEEE Trans. Circuits Syst. 2, Vol. 43, 422-433, Jun. 1996.
doi:10.1109/82.502315 Google Scholar

11. Angelides, E. and J. E. Diamessis, "A novel method for designing FIR digital filters with non-uniform frequency samples," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 42, 259-267, Feb. 1994. Google Scholar

12. Angelides, E., "A recursive frequency-sampling method for designing zero-phase FIR filters by nonuniform samples," IEEE Trans. Signal Processing, Vol. 6, 1461-1467, Jun. 1995.
doi:10.1109/78.388858 Google Scholar

13. Sutton, B. P., D. C. Noll, and J. A. Fessler, "Fast, iterative image reconstruction for MRI in the presence of field inhomogeneities," IEEE Trans. Med. Imag., Vol. 22, No. 2, 178-188, Feb. 2003.
doi:10.1109/TMI.2002.808360 Google Scholar

14. Sutton, B. P., J. A. Fessler, and D. Noll, "A min-max approach to the non-uniform N-D FFT for rapid iterative reconstruction of MR images," Proc. Int. Soc. Mag. Res. Med., 763, 2001. Google Scholar

15. Brouw, W. N., "Aperture synthesis," Methods in Computational Physics, Vol. 14, 131-175, B. Alder, S. Fernbach, and M. Rotenberg (eds.), 1975. Google Scholar

16. O'Sullivan, J. D., "A fast sinc function gridding algorithm for Fourier inversion in computer tomography," IEEE Trans. Med. Imag., Vol. 4, No. 4, 200-207, 1985.
doi:10.1109/TMI.1985.4307723 Google Scholar

17. Fourmont, K., "Non-equispaced fast Fourier transforms with applications to tomography," J. Fourier Anal. Appl., Vol. 9, No. 5, 431-450, 2003.
doi:10.1007/s00041-003-0021-1 Google Scholar

18. Lawton, W., "A new polar Fourier-transform for computer-aided tomography and spotlight synthetic aperture radar," IEEE Transactions on Acoustics Speech and Signal Processing, Vol. 36, No. 6, 931-933, Jun. 1988.
doi:10.1109/29.1609 Google Scholar

19. Kaveh, M. and M. Soumekh, "Computer-assisted diffraction tomography," Image Recovery: Theory and Application, 369-413, H. Stark (ed.), 1987. Google Scholar

20. Dutt, A. and V. Rokhlin, "Fast Fourier transforms for nonequispaced data," SIAM J. Sci. Comput., Vol. 14, 1368-1393, Nov. 1993.
doi:10.1137/0914081 Google Scholar

21. Dutt, A. and V. Rokhlin, "Fast Fourier transforms for nonequispaced data 2," Appl. Comput. Harmon. Anal., Vol. 2, 85-100, 1995.
doi:10.1006/acha.1995.1007 Google Scholar

22. Beylkin, G., "On the fast fourier-transform of functions with singularities," Appl. Comput. Harmon. Anal., Vol. 2, No. 4, 363-381, Oct. 1995.
doi:10.1006/acha.1995.1026 Google Scholar

23. Steidl, G., "A note on fast Fourier transforms for nonequispaced grids," Advances in Computational Mathematics, Vol. 9, 337-352, 1998.
doi:10.1023/A:1018901926283 Google Scholar

24. Potts, D., G. Steidl, and M. Tasche, "Fast Fourier transforms for nonequispaced data: A tutorial," Modern Sampling Theory: Mathematics and Applications, 249-274, J. J. Benedetto and P. Ferreira (eds.), Birkhauser, Boston, MA, 2001. Google Scholar

25. Bagchi, S. and S. K. Mitra, "The nonuniform discrete Fourier transform and its applications in filter design. 2 --- 2-D," IEEE Trans. Circuits Syst. 2, Vol. 43, 434-444, Jun. 1996.
doi:10.1109/82.502316 Google Scholar

26. Su, K. Y. and J. T. Kuo, "A two-dimensional nonuniform fast Fourier transform (2-D NUFFT) method and its applications to the characterization of microwave circuits," Asia-Pacific Microwave Conf., 801-804, Seoul, Korea, Nov. 4-7, 2003. Google Scholar

27. Su, K. Y. and J. T. Kuo, "Application of Two-Dimensional Non-uniform Fast Fourier Transform (2-D NUFFT) technique to analysis of shielded microstrip circuits," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 3, Mar. 2005. Google Scholar

28. Liu, Q. H., X. M. Xu, B. Tian, and Z. Q. Zhang, "Applications of nonuniform fast transform algorithms in numerical solutions of differential and integral equations," IEEE Trans. Geosci. Remote Sensing, Vol. 38, No. 4, 1551-1560, Jun. 2000.
doi:10.1109/36.851955 Google Scholar

29. Stoer, J. and R. Bullirsch, Introduction to Numerical Analysis, Springer-Verlag, 1980.

30. Yazici, A., I. Altas, and T. Ergenc, "2D polynomial interpolation: A symbolic approach with mathematica," Lecture Notes in Computer Science (LNCS), Vol. 3482, 463-471, O. Gervasi et al. (eds.), ICCSA, Springer-Verlag Berlin Heidelberg, 2005. Google Scholar

31. Board, J. and K. Schulten, "The fast multipole algorithm," Computing in Science and Engineering 2, Vol. 1, 76-79, 2000. Google Scholar

32. Raykar, V. C., "A short primer on the fast multipole method: FMM tutorial,", University of Maryland, College Park, Apr. 8, 2006. Google Scholar

33. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propagat. Mag., Vol. 35, 7-12, Jan. 1993.
doi:10.1109/74.250128 Google Scholar

34. Song, J. M. and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering," Microw. Opt. Technol. Lett., Vol. 10, 15-19, 1995. Google Scholar

35. Wei, X.-C., E. P. Li, and Y. J. Zhang, "Application of the improved finite element-fast multipole method on large scattering problems," Progress In Electromagnetics Research, Vol. 47, 49-60, 2004.
doi:10.2528/PIER03092501 Google Scholar

36. Sørensen, T. S., T. Schaeffter, K. Ø. Noe, and M. S. Hansen, "Accelerating the non-equispaced fast fourier transform on commodity graphics hardware," IEEE Transactions on Medical and Imaging, Vol. 27, No. 4, Apr. 2008. Google Scholar

37. Turner, L. R., "Inverse of the vandermonde matrix with applications," NASA, Washington, D.C., Aug. 1966. Google Scholar

38. Electe, A. H. and I. Yad-Shalom, "Fast multi-resolution algorithms for matrix vector multiplication,", Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, Virginia, Oct. 1992. Google Scholar

39. Nguyen, D. K., I. Lavall'ee, and M. Bui, "A general scalable implementation of fast matrix multiplication algorithms on distributed memory computers," Proceedings of the Sixth International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing and First ACIS International Workshop on Self-Assembling Wireless Networks (SNPD/SAWN'05), 2005. Google Scholar

40. Bond, D. M. and S. A. Vavasis, "Fast wavelet transforms for matrices arising from boundary elements methods: Tutorial,", Center for Applied Mathematics, Engineering and Theory Center, Cornell University, Ithaca, NY, Mar. 25, 1994. Google Scholar

41. "Fast multiplication of large matrices,", Wavelet Applications (Wavelet Toolbox), Matlab7.1. Google Scholar

42. Liu, Q. H. and X. Y. Tang, "Iterative algorithm for nonuniform inverse fast Fourier transform (NU-IFFT)," Electronics Letters, Vol. 34, No. 20, 1913-1914, 1998.
doi:10.1049/el:19981372 Google Scholar

Dr. Mohamed Ayari

Dr. Taoufik Aguili

Mr. Henri Baudrand