Interpolation of Non-Uniformly Sampled Sequences and Reconstruction of Sampled Sequences with Any Uniform Interval Based on Non-Uniform Sampling Theorem

Abstract

In this paper we psesent a new non-uniform sampling theorem for band-limited signals, together with an associated interpolation formula of non-uniformly sampled sequences, and propose a practical algorithm for reconstructing sampled sequences of any uniform interval from a non-uniform one by using the frequency sampling technique and FFT algorithm. After a brief review of the ordinary uniform sampling theorem, the non-uniform sampling theorem is given, together with an aliasing free condition being made clear. Based on the fundamentals, an interpolation formula of non-uniformly sampled sequences is derived and a practical implementation algorithm to reconstruct uniformly sampled sequences of any desired interval from a non-uniformly sampled version is proposed by way of the frequency sampling technique and FFT algorithm. The principle as well as the effectiveness of the proposed algorithm are ascertained through numerical experiments with sinusoidal and FM signals of finite bandwidths.