Numerical Algorithms

, Volume 68, Issue 4, pp 867–901 | Cite as

Design of a discrete algebraic robust differentiation FIR filter using an annihilator of the Z-transform; frequency response analysis and parameter tuning

  • Fabien Courreges
Original Paper


The seminal work of Mboup et al. [1] has opened a new approach of robust differentiator design based upon the concept of annihilator of the Laplace transform of a continuous input signal. Our work is an investigation of the derivation and analysis of a new discrete FIR estimator designed using this same concept. We have specifically considered a discrete input signal and derived an annihilator of its Z-transform. The resulting new estimator expression shows to be very simple to implement as two cascaded stages: 1. Signal smoothing with a low-pass filter; 2. Euler finite differentiation. We could also derive fast algorithms for the parameters tuning in case of ripple noise. Our experimental results show the ease of parameter tuning and efficacy of the estimator.


Robust discrete algebraic differentiator Annihilator of the signal’s Z-transform FIR digital differentiator Parameter tuning. 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Xlim Institute, Mechatronics teamUniversity of LimogesLimogesFrance

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