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Computing Derivatives of Noisy Signals Using Orthogonal Functions Expansions

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Adi Ditkowski

  2. Department of Engineering, Brown University, Providence, RI, 02912, USA

    Abhinav Bhandari & Brian W. Sheldon

Authors
  1. Adi Ditkowski
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  2. Abhinav Bhandari
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  3. Brian W. Sheldon
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Corresponding author

Correspondence to Adi Ditkowski.

Additional information

This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 1364/04) and the UNITED STATES-ISRAEL BINATIONAL SCIENCE FOUNDATION (grant No. 2004099).

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Ditkowski, A., Bhandari, A. & Sheldon, B.W. Computing Derivatives of Noisy Signals Using Orthogonal Functions Expansions. J Sci Comput 36, 333–349 (2008). https://doi.org/10.1007/s10915-008-9193-9

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  • DOI: https://doi.org/10.1007/s10915-008-9193-9

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