Polynomial Interpolation of Randomly Sampled Bandlimited Functions and Processes

Abstract

This paper considers the performance of Lagrange polynomial interpolation and extrapolation of randomly sampled bandlimited functions and processes; the sampling instants $\{ t_n \}$ belong to a broad class of stationary point processes which includes periodic and Poisson sampling schemes. We establish mean-square and probability-one convergence for such interpolators. We also derive explicit truncation error bounds and explore their dependence on the sampling rate, the number of samples used, and the irregularity of the sampling instants.