Polynomial Extrapolation Toward Low Frequencies of the Spectrum of Gated Ultrasonic Echoes for Deconvolution: Application to Defects in Solids

摘要

In order to get a correct evaluation of the response function of a scatterer in the time domain, a deconvolution operation is necessary. This operation is made difficult by the absence of information at low frequencies. We present a technique here whose purpose is the reconstruction of the low frequency part by extrapolation. Practically, the spectrum is sampled at given points and a polynomial passing by the same points is constructed. The samples in the unknown part are determined by trying different values and looking for a minimum distance between the actual spectrum and the approximating polynomial. Numerical results and an actual ultrasonic signal are presented.