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 one 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