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

• Published in: Numerical algorithms Vol. 68; no. 4; pp. 867 - 901
• Main Author: Courreges, Fabien
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2015; Springer Nature B.V; Springer Verlag
• Subjects: Algebra; Algorithms; Computer Science; Design engineering; Differentiation; Engineering Sciences; Estimators; FIR filters; Frequency response; Low pass filters; Mathematical models; Numeric Computing; Numerical Analysis; Original Paper; Parameters; Ripples; Robustness; Signal and Image processing; Theory of Computation; Tuning; Z transforms; Robust discrete algebraic differentiator; FIR digital differentiator; Annihilator of the signal’s Z-transform; Parameter tuning
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-014-9875-3

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.