Estimation of signal spectrum support using periodic nonuniform sampling

Abstract

We estimate the signal spectrum support of band-limited signal using periodic nonuniform sampling. First we justify the relation between discrete samples and spectrum repetition of a signal using Poisson summation formula. From this relation, we derive a criterion that measures the level of aliasing which we want to minimize. Second part is devoted to implementing the problem to find actual PNS sequences. We introduce very natural assumptions that allow us the finite set of solutions. After finding the optimal PNS sequence, we do the spectral analysis of a band-limited signal of which precise spectrum support is not known. Finally we can estimate the spectral support of the signal through the graph of frequency domain representation.