Approximation of discontinuous signals by sampling Kantorovich series

TL;DR

This paper investigates the approximation capabilities of sampling Kantorovich operators for discontinuous signals, estimates their approximation rate for continuous signals, explores linear prediction from past samples, and examines the impact of duration-limited kernels with illustrative examples.

Contribution

It provides new insights into the behavior and approximation rate of sampling Kantorovich operators for discontinuous signals and analyzes the role of duration-limited kernels.

Findings

Sampling Kantorovich operators effectively approximate discontinuous signals.

The approximation rate is quantified for uniformly continuous and bounded signals.

Duration-limited kernels influence the approximation process significantly.

Abstract

In this paper, the behavior of the sampling Kantorovich operators has been studied, when discontinuous signals are considered in the above sampling series. Moreover, the rate of approximation for the family of the above operators is estimated, when uniformly continuous and bounded signals are considered. Further, also the problem of the linear prediction by sampling values from the past is analyzed. At the end, the role of duration-limited kernels in the previous approximation processes has been treated, and several examples have been provided.