Direct Extrapolation of a Causal Signal Using Low-Frequency and Early-Time Data Based on Integral Equations

摘要

In this paper we provide two direct procedures to extrapolate the early-time and the low-frequency response of a causal signal simultaneously in the time-and frequency domain. We show that the extrapolation introduced by Adve and Sarkar is equivalent to a Neumann-series solution of an integral equation of the second kind. It is further shown that this iterative Neumann expansion is an error-reducing method. We propose to solve this integral equation efficiently by employing a conjugate gradient iterative scheme. The convergence of this scheme is also demonstrated. Finally, a numerical example is presented and the performances of the two direct methods are compared.