Foldings of Periodic Nonuniform Samplings

Periodic Nonuniform Samplings of order <tex-math notation="LaTeX">N </tex-math> (PNS <tex-math notation="LaTeX">N </tex-math> ) are interleavings of periodic samplings. For a base period <tex-math notation="LaTeX">T </tex-math> , simple algorithms can be used to reconstruct functions of spectrum included in an union <tex-math notation="LaTeX">Δ </tex-math> of <tex-math notation="LaTeX">N </tex-math> intervals <tex-math notation="LaTeX">δ ₖ </tex-math> of length <tex-math notation="LaTeX">$1/T$ </tex-math> . In this brief we study the behavior of these algorithms when applied to any function. We prove that they result in <tex-math notation="LaTeX">N </tex-math> (or less) foldings on <tex-math notation="LaTeX">Δ </tex-math> , each of <tex-math notation="LaTeX">δ ₖ </tex-math> holding at most one folding.