Universal truncation error upper bounds in sampling restoration

TL;DR

This paper derives universal upper bounds for truncation errors in sampling restoration for Bernstein function classes, applicable even when the decay rate of sampled functions is unknown, and explores extremal properties of sinc series.

Contribution

It introduces universal truncation error bounds for the WKS sampling sum applicable to Bernstein classes without decay rate knowledge.

Findings

Derived universal pointwise truncation error bounds.

Analyzed extremal properties of sinc function series.

Discussed regular sampling scenarios.

Abstract

Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker--Kotel'nikov--Shannon (WKS) sampling restoration sum for Bernstein function classes $B_{\pi,d}^q,\, q>1,\, d\in \mathbb N$, when the decay rate of the sampled functions is unknown. The case of regular sampling is discussed. Extremal properties of related series of sinc functions are investigated.