Topic
Bessel filter
About: Bessel filter is a research topic. Over the lifetime, 656 publications have been published within this topic receiving 16808 citations.
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TL;DR: In this paper, the authors studied the application of the fractional Hankel transformation (FrHT) in solving generalized n th order linear nonhomogeneous ordinary differential equations and the continuous fractional Bessel wavelet transformation.
Abstract: The main objective of this paper is to study the fractional Hankel transformation and the continuous fractional Bessel wavelet transformation and some of their basic properties. Applications of the fractional Hankel transformation (FrHT) in solving generalized n th order linear nonhomogeneous ordinary differential equations are given. The continuous fractional Bessel wavelet transformation, its inversion formula and Parseval’s relation for the continuous fractional Bessel wavelet transformation are also studied. MSC:46F12, 26A33.
17 citations
TL;DR: Multi-resolution quadrature rules based on hybrid functions and Haar wavelets are used as supporting tools to handle the case of singularity of the meshless collocation method.
17 citations
TL;DR: In this article, the authors extended the Bessel functions from the real number field to the complex number field and defined a new type of Bessel function, called the phased Bessel Function.
Abstract: In the study of photon-state transitions, we found a natural extension of the first kind of Bessel functions that extends both the range and domain of the Bessel functions from the real number field to the complex number field. We term the extended Bessel functions as phased Bessel functions. This extension is completely different from the traditional “analytical extension”. The new complex Bessel functions satisfy addition, subtraction, and recurrence theorems in a complex range and a complex domain. These theorems provide short cuts in calculations. The single-phased Bessel functions are generalized to multiple-phased Bessel functions to describe various photon-state transitions.PACS Nos.: 02.30.Gp, 32.80.Rm, 42.50.Hz
17 citations
TL;DR: This paper focuses on the problem of delay-range-dependent L2–L∞ filter design for stochastic systems with time-varying delay, and a sufficient condition is formulated in terms of linear matrix inequalities (LMIs), which guarantees the existence of a linear filter.
Abstract: This paper focuses on the problem of delay-range-dependent L 2---L ? filter design for stochastic systems with time-varying delay. The time delay varies in an interval. A delay-range-dependent sufficient condition is formulated in terms of linear matrix inequalities (LMIs), which guarantees the existence of a linear filter. The proposed filter ensures that the filtering error system is stochastically asymptotically stable and that its L 2---L ? performance satisfies a prescribed level. The corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
17 citations
TL;DR: A new filter with transient characteristics that are comparable to those of the modified Paynter filter but with superior high-frequency attenuation is designed and constructed, a modified seventh-order Bessel filter.
Abstract: Platt, Ronald S., Eric A. Hajduk, Manuel Hulliger, and Paul A. Easton. A modified Bessel filter for amplitude demodulation of respiratory electromyograms. J. Appl. Physiol. 84(1): 378–388, 1998.—We...
16 citations