A novel technique for extrapolation of transient response using early-time and low-frequency data is proposed in this paper. An improved extrapolation scheme using approximate prolate series is presented to obtain a transient electromagnetic response. The approximate prolate series, which has an approximately band-limited and sub-domain nature, is a better choice for extrapolating the time-domain electromagnetic response than orthogonal polynomials, such as Laguerre functions and Hermite functions. A novel regularization method based on truncated generalized SVD is also proposed to solve the ill-posed extrapolation problems, which make the extrapolation technique much less sensitive to noise in the known part of the response. Some numerical results are presented to illustrate the effectiveness and accuracy of the proposed method in extrapolation of transient electromagnetic problems.
2. Rao, M. M., T. K. Sarkar, R. S. Adve, T. Anjali, and J. F. Callejon, "Extrapolation of electromagnetic responses from conducting objectsin time and frequency domains," IEEE Trans. Microw. Theory Tech., Vol. 47, 1964-1974, Oct. 1999.
doi:10.1109/22.795070
3. Sarkar, T. K. and J. Koh, "Generation of a wide-band electromagnetic response through a Laguerre expansion using early-time and low- frequency data," IEEE Trans. Microw. Theory Tech., Vol. 50, 1408-1416, May 2002.
doi:10.1109/22.999156
4. Yuan, M., J. Koh, T. K. Sarkar, W. Lee, and M. Salazar-Palma, "A comparison of performance of three orthogonal polynomials in extraction of wide-band response using early time and low frequency data," IEEE Trans. Antennas Propag., Vol. 53, 785-792, Feb. 2005.
doi:10.1109/TAP.2004.841330
5. Yuan, M., A. De, T. K. Sarkar, J. Koh, and B. H. Jung, "Conditions for generation of stable and accurate hybrid TD-FD MoM solutions," IEEE Trans. Antennas Propag., Vol. 54, No. 6, 2552-2563, Jun. 2006.
6. Frye, J. M. and A. Q. Martin, "Extrapolation of time and frequency responses of resonant antennas using damped sinusoids and orthogonal polynomials," IEEE Trans. Antennas Propag., Vol. 56, No. 4, 933-943, Apr. 2008.
doi:10.1109/TAP.2008.919195
7. Frye, J. M. and A. Q. Martin, "Time and frequency bias in extrapolating wideband responses of resonant structures," IEEE Trans. Antennas Propag., Vol. 57, No. 12, 3934-3941, Dec. 2009.
doi:10.1109/TAP.2009.2033285
8. Zhao, H. and Y. Zhang, "Extrapolation of wideband electromagnetic response using sparse representation," representation, Vol. 60, No. 2, 1026-1034, Feb. 2012.
9. Hansen, P. C., "Regularization, GSVD and truncated GSVD," BIT, Vol. 29, No. 3, 491-504, Sep. 1989.
doi:10.1007/BF02219234
10. Knab, J. J., "Interpolation of band-limited functions using the approximate prolate series," IEEE Trans. Inform. Theory, Vol. 25, 717-720, 1979.
doi:10.1109/TIT.1979.1056115
11. Tikhonov, A. N. and V. Y. Arsenin, Solutions of Ill-posed Problems, Winston & Sons, Washington, D.C., 1977.
12. Hansen, P. C., "Analysis of discrete ill-posed problems by means of the L-curve," SIAM Review, Vol. 34, No. 4, 561-580, Dec. 1992.
doi:10.1137/1034115
Submit
