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Journal of Scientific Computing

, Volume 36, Issue 3, pp 333–349 | Cite as

Computing Derivatives of Noisy Signals Using Orthogonal Functions Expansions

  • Adi Ditkowski
  • Abhinav Bhandari
  • Brian W. Sheldon
Article

Abstract

In many applications noisy signals are measured. These signals have to be filtered and, sometimes, their derivative has to be computed.

In this paper a method for filtering the signals and computing the derivatives is presented. This method is based on expansion onto transformed Legendre polynomials.

Numerical examples demonstrate the efficacy of the method as well as the theoretical estimates.

Keywords

Noise filtering Spectral methods Orthogonal polynomials 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Adi Ditkowski
    • 1
  • Abhinav Bhandari
    • 2
  • Brian W. Sheldon
    • 2
  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Department of EngineeringBrown UniversityProvidenceUSA

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