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Science China Mathematics

, Volume 55, Issue 12, pp 2481–2491 | Cite as

The construction of generalized B-spline low-pass filters related to possibility density

  • QiuHui Chen
  • LuoQing LiEmail author
  • Helmuth Malonek
Articles

Abstract

Starting from piecewise constant functions, a novel family of generalized symmetric B-splines, with realizable ideal low-pass filters, are constructed. The first order generalized B-spline low-pass filter is closely related to functions analytic in a neighborhood of the unit disc and the generalized sinc functions. The properties of this kind of low-pass filters are investigated. The behavior of the generalized B-spline low-pass filter related to normalized Gaussian distribution is considered.

Keywords

low-pass filter generalized B-spline analytic function Gaussian distribution 

MSC(2010)

42A38 44A15 62P30 65R10 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Cisco School of InformaticsGuangdong University of Foreign StudiesGuangzhouChina
  2. 2.Faculty of Mathematics and Computer SciencesHubei UniversityWuhanChina
  3. 3.Department of MathematicsUniversity of AveiroAveiroPortugal

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