Nonuniform sampling: bandwidth and aliasing

Abstract. For spectroscopic measurements there are good reasons why one might consider using nonuniformly nonsimultaneously sampled complex data. The pri-mary one is that the eective bandwidth, the largest spectral window free of aliases, can be much wider than with uniformly sampled data. In this paper we discuss nonuniformly nonsimultaneously sampled data, describe how these data are tradi-tionally analyzed, analyze them using probability theory and show how probability theory generalizes the discrete Fourier transform: rst for uniformly sampled data, then for nonuniformly sampled data and nally for nonuniformly nonsimultane-ously sampled data. These generalizations demonstrate that aliases are not so much removed by nonuniform nonsimultaneous sampling as they are moved to much higher frequencies. 1