SIMULTANEOUS TIME-DOMAIN AND FREQUENCY-DOMAIN EXTRAPOLATION

In this paper, given the early-time response and the low-frequency res ponse of a causal system, we simultaneously extrapolate them in the ti me and frequency domains. The approach is iterative and is based on a simple discrete Fourier transform. Simultaneous extrapolation in time and frequency domains is further enhanced by using the matrix pencil t echnique in the time domain and the Cauchy method in the frequency dom ain. The results are further enhanced through the Hilbert transform, h ence enforcing the physical constraints of the system and thereby guar anteeing a causal extrapolation in time. It is, therefore, possible to generate information over a larger domain from limited data. It is im portant to note that through this extrapolation, no new information is created. The early-time and low-frequency data are complementary and contain all the desired information. The key is to extract this inform ation in an efficient and accurate manner.