### Abstract

The objective of this paper is to present a methodology for the analysis of electromagnetic systems irradiated by an ultra-short ultra-wideband electromagnetic pulse. This is accomplished through the use of a hybrid method that involves simultaneous generation of early time and low frequency information. These two data sets, namely early time and low frequency, in the original and transform domains are not only easy to generate, but also contain all the necessary mutually complementary information to electromagnetically characterize the system. This assumes that a sufficient record length is available in both domains. A criterion is provided to assess whether the record lengths are sufficiently long. Utilizing orthogonal associate Hermite functions, a time domain signal representing the electromagnetic quantity of interest (be it current or the scattered electromagnetic fields) can be expressed as a weighted sum of these quantities in an efficient way. The associate Hermite functions are orthonormal and are expressed through the Hermite polynomials. The frequency domain response can also be characterized by the same set of functions weighted by the same sets of coefficients, as the Hermite polynomials are the eigenfunctions of the Fourier transform operator. The available data in both domains are then simultaneously used to solve for the unknown weights. Once these coefficients are known the data can be simultaneously extrapolated in both the time and frequency domains. Computational load for the electromagnetic analysis for this method is quite modest compared to solving the electromagnetic analysis problem exclusively in either domain. Numerical examples are presented to illustrate the application of this hybrid methodology.

Original language | English (US) |
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Pages (from-to) | 1757-1768 |

Number of pages | 12 |

Journal | Measurement Science and Technology |

Volume | 12 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2001 |

### Keywords

- Associate Hermite functions
- Hybrid method
- Marching on in time
- Maxwell's equation

### ASJC Scopus subject areas

- Instrumentation
- Engineering (miscellaneous)
- Applied Mathematics

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## Cite this

*Measurement Science and Technology*,

*12*(11), 1757-1768. https://doi.org/10.1088/0957-0233/12/11/302