Reconstruction of nonuniformly sampled periodic signals: algorithms and stability analysis

Abstract

This paper introduces two new algorithms for perfect reconstruction of a periodic bandlimited signal from its nonuniform samples. We analyze the advantages and disadvantages of each method and discuss their properties. Based on the theory of frames, we also analyze the stability of the algorithms. Some special structures of the sampling points are investigated and we show that uniform sampling results in the most stable and simple reconstruction algorithm. We also provide experimental evidence to support our theoretical results.