Numerical Algorithms

, Volume 50, Issue 4, pp 439–467 | Cite as

Numerical differentiation with annihilators in noisy environment

  • Mamadou MboupEmail author
  • Cédric Join
  • Michel Fliess
Original Paper


Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented.


Numerical differentiation Operational calculus Orthogonal polynomials Linear filtering 

Mathematics Subject Classifications (2000)

65D25 44A40 44A10 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.UFR Mathématiques et Informatique, CRIP5Université Paris DescartesParis cedex 06France
  2. 2.CRAN (CNRS-UMR 7039)Université Henri Poincaré (Nancy I)Vandœuvre-lès- NancyFrance
  3. 3.Équipe MAX, LIX (CNRS-UMR 7161)École polytechniquePalaiseauFrance
  4. 4.EPI ALIEN INRIAParisFrance

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