Sampling and recovery using multiquadrics

Abstract

We survey recent results in the subject of interpolating bandlimited functions from their samples at both uniform and nonuniform sets via translates of a family of multiquadrics. Recovery of the original function is considered by means of a limiting process which changes a shape parameter associated with the multiquadric function. We also discuss some ways in which approximation rates can be found as well as extensions of the results to interpolation schemes which use other radial basis functions.