A linear, time-varying system framework for noniterative discrete-time band-limited signal extrapolation

A technique for the analysis and design of noniterative algorithms for discrete-time, band-limited signal extrapolation is described. The approach involves modeling the extrapolation process as a linear, time-varying (LTV) system, or filter. Together with a previously developed Fourier theory for LTV systems, this model provides a frequency-domain transfer function representation for the extrapolation system. This representation serves as a powerful tool for characterizing and comparing the reconstruction properties of several well-known least squares optimal algorithms for band-limited extrapolation. Moreover, the frequency-domain setting provides a conceptually attractive means for understanding the process of extrapolation itself. Additionally, a least squares approximation methodology for designing LTV filters for band-limited extrapolation is developed. The design technique is shown to unify a broad class of algorithms for extrapolating discrete-time data and, further, to provide a means for designing new and improved extrapolation algorithms.>