EMP Signal Reconstruction Using Associated-Hermite Orthogonal Functions

This letter presents a novel signal reconstruction technique using the associated-Hermite (AH) orthogonal functions. By adjusting the scaling factor and the time shift, a serious of AH functions with limited order can be used to approximate typical electromagnetic pulse signal. Because AH functions are also eigenfunctions of the Fourier transform operator, the transfer function of an unknown system can be described by the AH expansion coefficient of the input and output waveforms. This transfer function can be further used to reconstruct the measurement signal deformed by the nonideal features of the system. Compared to traditional FFT method, the transfer function obtained by AH expansion is a parametric model with higher stability. This method is applied to reconstruct the output of a coaxial high-voltage pulse probe, and the reconstructed waveforms are compared to the results obtained by FFT method and the system identification method.