Parameter Estimation of Double Exponential Pulses (EMP, UWB) With Least Squares and Nelder Mead Algorithm

Abstract

Transient test pulses like electromagnetic pulse and ultrawide-band are commonly described by rise time t/sub r/, pulse length t/sub fwhm/ and the maximum amplitude E/spl circ/. Simulating the effects of varying pulses an analytical description of the pulses is necessary, which is given by a double exponential form with the parameters /spl alpha/, /spl beta/ and E/sub 0/. This paper describes the link between the parameters t/sub r/, t/sub fwhm/ and E/spl circ/ on the one side and the analytical parameters /spl alpha/, /spl beta/ and E/sub 0/ on the other side. It is shown that the Nelder Mead simplex algorithm in combination with the least squares method is appropriate to determine an analytical relationship between these parameters. There with extensive analysis of double exponential pulse shapes with far-ranging parameters is possible in a considerably smaller computing time.