volume | PIER Journals

Abstract

Generation of a wide-band response using partial information from the time domain (TD) data and frequency domain (FD) data has been accomplished in this paper through the use of three different orthogonal functions, such as the continuous Laguerre functions, the Bessel-Chebyshev functions, and the associate Hermite functions. In this hybrid approach, one can generate the early-time response using the method of marching-on-in-time (MOT) and use the method of moment (MOM) to generate the middle-frequency response, as the low-frequency data may be unstable. Since the early-time and the middle-frequency data are mutually complimentary, they can provide the missing low- and high-frequency response and the late-time response, respectively. Even though obtaining middle-frequency response from an object needs more computation time than the low-frequency response, this approach has better performance for the interpolation and extrapolation of a wide-band response.

1. Adve, R. S. and T. K. Sarkar, "Simultaneous time and frequency domain extrapolation," IEEE Trans. Antennas Propagat., Vol. 46, No. 4, 484-493, Apr. 1998.
doi:10.1109/8.664111

2. Rao, M. M., T. K. Sarkar, R. S. Adve, T. Anjali, and J. F. Callejon, "Extrapolation of electromagnetic responses from conducting objects in time and frequency domains," IEEE Trans. Microwave Theory Tech., Vol. 47, No. 10, 1964-1974, Oct. 1999.
doi:10.1109/22.795070

3. Rao, M. M., T. K. Sarkar, T. Anjali, and R. S. Adve, "Simultaneous extrapolation in time and frequency domains using Hermite expansions," IEEE Trans. Antennas Propagat., Vol. 47, No. 6, 1108-1115, Jun. 1999.
doi:10.1109/8.777138

4. 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. Microwave Theory Tech., Vol. 50, No. 5, 1408-1416, May 2002.
doi:10.1109/22.999156

5. Yuan, M., T. K. Sarkar, B. H. Jung, Z. Ji, and M. Salazar-Palma, "Use of discrete Laguerre sequences to extrapolate wide-band response from early-time and low-frequency data," IEEE Trans. Microwave Theory Tech., Vol. 52, No. 7, 1740-1750, Jul. 2004.
doi:10.1109/TMTT.2004.830490

6. 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. Microwave Theory Tech., Vol. 54, No. 6, 2552-2563, Jun. 2006.
doi:10.1109/TMTT.2006.875823

7. Lee, W., T. K. Sarkar, J. Koh, H. Moon, and M. Salazar-Palma, "Generation of a wide-band response using early-time and middle-frequency data through the Laguerre functions," Progress In Electromagnetics Research Letters, Vol. 30, 115-123, Mar. 2012.
doi:10.2528/PIERL12020204

8. Poularikas, A. D., The Transforms and Applications Handbook, 2nd Ed., Chs. 1, 2, 5, 6, 15, CRC Press and IEEE Press, 2000.
doi:10.1201/9781420036756

9. Arnold, C. R., Laguerre functions and the Laguerre network --- Their properties and digital simulation, Technical Note: 1966-28, Lincoln Laboratory, Massachusetts Institute of Technology, May 1966.

10. Mason, J. C. and D. C. Handscomb, Chebyshev Polynomials, CRC Press LLC, 2003.

11. Lo Conte, L. R., R. Merletti, and G. V. Sandri, "Hermite expansions of compact support waveforms: Applications to myoelectic signals," IEEE Trans. Biomed. Eng., Vol. 41, No. 12, 1147-1159, Dec. 1994.
doi:10.1109/10.335863

12. Watkins, D. S., Fundamentals of Matrix Computation, 3rd Ed., Ch. 4, Wiley, 2010.

13. HOBBIES (Higher Order Basis Based Integral Equation Solver), http://www.em-hobbies.com/.

14. 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 Propagat., Vol. 53, No. 2, 785-792, Feb. 2005.
doi:10.1109/TAP.2004.841330

Dr. Woojin Lee

Professor Tapan Kumar Sarkar

Dr. Jinhwan Koh

Dr. Hongsik Moon

Dr. Magdalena Salazar-Palma