Approximation of discontinuous functions by Kantorovich exponential sampling series

TL;DR

This paper analyzes how Kantorovich exponential sampling series approximate discontinuous functions, providing theoretical results and numerical validation for their effectiveness in signal approximation and prediction.

Contribution

It introduces new approximation theorems for discontinuous signals using Kantorovich exponential sampling series and develops a linear prediction method based on past samples.

Findings

Established a representation lemma for the series.

Proved approximation theorems involving logarithmic modulus of smoothness.

Validated the approximation through numerical simulations.

Abstract

The Kantorovich exponential sampling series at jump discontinuities of the bounded measurable signal f has been analysed. A representation lemma for the series is established and using this lemma certain approximation theorems for discontinuous signals are proved. The degree of approximation in terms of logarithmic modulus of smoothness for the series is studied. Further a linear prediction of signals based on past sample values has been obtained. Some numerical simulations are performed to validate the approximation of discontinuous signals f by the sampling series.