Estimation of the Mathematical Parameters of Double-Exponential Pulses Using the Nelder-Mead Algorithm

• Published in: IEEE transactions on electromagnetic compatibility Vol. 52; no. 4; pp. 1060 - 1062
• Main Authors: Magdowski, M, Vick, R
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-11-2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Approximation; Approximation algorithms; Detection, estimation, filtering, equalization, prediction; Double-exponential pulse; Electromagnetic compatibility; Estimation error; Exact sciences and technology; Exact solutions; high-altitude electromagnetic pulse; Information, signal and communications theory; Least squares approximation; Least squares method; Mathematical analysis; Mathematical models; Nelder-Mead; Parameter estimation; pulsewidth; rise time; Signal and communications theory; Signal, noise; Studies; Telecommunications and information theory; Ultrawideband; ultrawideband pulse; High altitude; Pulse width; Parameter estimation; Rise time; high-altitude electromagnetic pulse; pulsewidth; Electromagnetic compatibility; Electromagnetic pulse; Algorithm; Exponential function; Ultra wide band; Computation time; Nelder-Mead; Least squares method; Simplex method; ultrawdeband pulse; Approximation error; Double-exponential pulse; Pulse shape
• ISSN: 0018-9375; 1558-187X
• DOI: 10.1109/TEMC.2010.2052621

Transient pulses for electromagnetic compatibility problems, such as the high-altitude electromagnetic pulse and ultrawideband pulses, are often described by a double-exponential pulse. Such a pulse shape is specified physically by the three characteristic parameters rise time tr , pulsewidth t fwhm (full-width at half-maximum), and maximum amplitude E max . The mathematical description is a double-exponential function with the parameters α, β, and E 0 . In practice, it is often necessary to transform the two groups of parameters into each other. This paper shows a novel relationship between the physical parameters tr and t fwhm on the one hand and the mathematical parameters α and β on the other. It is shown that the least-squares method in combination with the Nelder-Mead simplex algorithm is appropriate to determine an approximate closed-form formula between these parameters. Therefore, the extensive analysis of double-exponential pulses is possible in a considerably shorter computation time. The overall approximation error is less than 3.8%.