On Some Stability and Interpolatory Properties of Nonuniform Sampling Expansions

This paper treats the Lagrange interpolation and stability properties of sampling expansions for bandlimited functions. It deals specifically with extensions of the uniform sampling expansion of Whittaker and Shannon. In general, sampling expansions of the Lagrange interpolation type for bandlimited signals exist for large classes of sampling sequences; however, such expansions are not necessarily stable in the sense that small corruptions in the amplitudes of sample values may not lead to small changes in the reconstructed function. The concept of a stable sampling expansion is defined. Two specific classes of nonuniform stable sampling expansions are considered. A well-known example of a sampling expansion which is not stable is given.