Approximation of Discontinuous Signals by Exponential Sampling Series

TL;DR

This paper investigates how exponential sampling series approximate signals with jump discontinuities, providing theoretical analysis, rate of convergence, error estimates, and graphical illustrations.

Contribution

It introduces a representation lemma and analyzes the approximation of discontinuous signals by exponential sampling series, including error bounds and practical visualizations.

Findings

Established approximation of jump discontinuities by exponential sampling series.

Derived rate of approximation using logarithmic modulus of continuity.

Analyzed round-off and time-jitter errors in the sampling process.

Abstract

We analyse the behaviour of the exponential sampling series $S_{w}^{\chi}f$ at jump discontinuity of the bounded signal $f.$ We obtain a representation lemma that is used for analysing the series $S_{w}^{\chi}f$ and we establish approximation of jump discontinuity functions by the series $S_{w}^{\chi}f.$ The rate of approximation of the exponential sampling series $S_{w}^{\chi}f$ is obtained in terms of logarithmic modulus of continuity of functions and the round-off and time-jitter errors are also studied. Finally we give some graphical representation of approximation of discontinuous functions by $S_{w}^{\chi}f$ using suitable kernels.