Sampling bessel functions and bessel sampling
Dragana Jankov Maširević, Tibor K. Pogány, Arpad Bariez, Aurél Galántai
Abstract
Dragana Jankov Maširević, Tibor K. Pogány, Arpad Bariez, Aurél Galántai
Abstract
The main aim of this article is to establish summation formulae in form of sampling expansion series for Bessel functions Yv, Iv; and Kv, and obtain sharp truncation error upper bounds occurring in the Y-Bessel sampling series approximation. The principal derivation tools are the famous sampling theorem by Kramer and various properties of Bessel and modified Bessel functions which lead to the so-called Bessel sampling when the sampling nodes of the initial signal function coincide with a set of zeros of different cylinder functions.
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The main aim of this article is to establish summation formulae in form of sampling expansion series for Bessel functions Yv, Iv; and Kv, and obtain sharp truncation error upper bounds occurring in the Y-Bessel sampling series approximation. The principal derivation tools are the famous sampling theorem by Kramer and various properties of Bessel and modified Bessel functions which lead to the so-called Bessel sampling when the sampling nodes of the initial signal function coincide with a set of zeros of different cylinder functions.
Key concepts: Bessel function, Bessel process, Cylindrical harmonics, Bessel polynomials, Sampling (signal processing), Mathematics, Bessel's inequality, Truncation (statistics)