Approximation by nonuniform sampling series and multiresolution analysis

The paper discusses the approximation of duration-limited signals by uniform or nonuniform sampling series, whose kernels are the reproducing kernels of a multiresolution analysis of L₂. We give an upper bound for the approximation error, which does not depend on the distribution of the sampling points. Since the approximating series is a finite sum, and the sampling points can be nonuniformly distributed, our results account for truncation and jitter errors. There are surprisingly few results on the approximation of nonbandlimited signals by nonuniform sampling series, a fact that adds to the interest of the results