On Nyquist-Shannon Theorem with one-sided half of sampling sequence

TL;DR

This paper demonstrates that a band-limited function can be reconstructed from only one side of an oversampling sequence, extending the classical Nyquist-Shannon theorem to semi-infinite sampling.

Contribution

It introduces a novel result that allows function recovery from a one-sided sampling sequence, broadening the applicability of classical sampling theory.

Findings

Function can be recovered from one-sided semi-infinite sampling series.

Same frequency bounds as classical theorem apply.

Extension of Nyquist-Shannon theorem to semi-infinite sequences.

Abstract

The classical sampling Nyquist-Shannon-Kotelnikov theorem states that a band-limited continuous time function can be uniquely recovered without error from a infinite two-sided sampling series taken with a sufficient frequency. This short note shows that the function can be recovered from any one-sided semi-infinite half of any oversampling series, with the same boundary for admissible frequencies as in the classical theorem.