On the estimation of the bandwidth of nonuniformly sampled signals

In many applications signals can only be sampled at nonuniformly spaced points. For a reliable reconstruction of the signal from its samples we require knowledge of the bandwidth of the signal, which however is often not known a priori. Therefore robust and efficient methods are needed that allow to estimate the bandwidth of a signal from nonuniform spaced, noisy samples. We present two procedures for bandwidth estimation. The first method is based on the discrete Bernstein inequality and Newton's divided differences and is computationally very efficient. The second method requires somewhat more computational effort, since it simultaneously estimates the bandwidth and provides a reconstruction of the signal. It is based on a multi-scale conjugate gradient algorithm for the solution of a nested sequence of Toeplitz systems and is particularly useful in case of noisy data. Examples from various applications demonstrate the performance of the proposed methods.