Exponential sampling with a multiplier

Bardaro C, Mantellini I, Schmeißer G (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Sampling Theory, Signal Processing, and Data Analysis Birkhäuser

Book Volume: 21

Article Number: 8

Journal Issue: 1

DOI: 10.1007/s43670-023-00048-8

Abstract

The exponential sampling formula has some limitations. By incorporating a Mellin bandlimited multiplier, we extend it to a wider class of functions with a series that converges faster. This series is a generalized exponential sampling series with some interesting properties. Moreover, under a side condition, any generalized exponential sampling series that is interpolating can be generated by a Mellin bandlimited multiplier. For an error analysis, we consider a truncated series with 2 N+ 1 terms and look for a highest speed of convergence as N→ ∞. We show by using a certain non-bandlimited multiplier, which introduces in addition an aliasing error, that we can achieve a higher rate of convergence to the function, namely O(e^-^α^N) with α> 0 , than with the truncated series of an exact formula. The results are illustrated by three examples.

Authors with CRIS profile

Gerhard Schmeißer Department Mathematik

Involved external institutions

Università degli Studi di Perugia

Italy (IT)

How to cite

APA:

Bardaro, C., Mantellini, I., & Schmeißer, G. (2023). Exponential sampling with a multiplier. Sampling Theory, Signal Processing, and Data Analysis, 21(1). https://dx.doi.org/10.1007/s43670-023-00048-8

MLA:

Bardaro, Carlo, Ilaria Mantellini, and Gerhard Schmeißer. "Exponential sampling with a multiplier." Sampling Theory, Signal Processing, and Data Analysis 21.1 (2023).

BibTeX: Download