Foldings of Periodic Nonuniform Samplings

Abstract

Periodic Nonuniform Samplings of order $N$ (PNS $N$ ) are interleavings of periodic samplings. For a base period $T$ , simple algorithms can be used to reconstruct functions of spectrum included in an union $\Delta $ of $N$ intervals $\delta _{k}$ of length $1/T$ . In this brief we study the behavior of these algorithms when applied to any function. We prove that they result in $N$ (or less) foldings on $\Delta $ , each of $\delta _{k}$ holding at most one folding.