Exponential sampling with a multiplier

Bardaro C, Mantellini I, Schmeißer G (2023)

Publication Type: Journal article

Publication year: 2023


Book Volume: 21

Article Number: 8

Journal Issue: 1

DOI: 10.1007/s43670-023-00048-8


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-αN) with α> 0 , than with the truncated series of an exact formula. The results are illustrated by three examples.

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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


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

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