Design of a discrete algebraic robust differentiation FIR filter using an annihilator of the Z-transform; frequency response analysis and parameter tuning
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 thi...
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| Published in | Numerical algorithms Vol. 68; no. 4; pp. 867 - 901 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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01.04.2015
Springer Nature B.V Springer Verlag |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Courreges, Fabien |
| Author_xml | – sequence: 1 givenname: Fabien surname: Courreges fullname: Courreges, Fabien email: fabien.courreges@unilim.fr organization: Xlim Institute, Mechatronics team, University of Limoges |
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| Cites_doi | 10.1021/ac60214a047 10.1016/S0021-9800(69)80045-1 10.1016/j.ijforecast.2006.03.001 10.3182/20090706-3-FR-2004.00256 10.3182/20090706-3-FR-2004.00239 10.1109/CDC.2009.5400719 10.1109/41.681239 10.2307/2325085 10.1007/s11075-008-9236-1 10.1504/IJMIC.2008.020996 10.1016/0165-1684(90)90012-N 10.1109/TAC.1977.1101671 10.1016/j.crma.2006.02.037 10.1109/MED.2007.4433728 10.1109/MED.2010.5547743 10.1109/CCA.2007.4389252 10.1093/ietfec/e90-a.8.1511 10.1049/el:19991183 |
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| Keywords | Robust discrete algebraic differentiator FIR digital differentiator Annihilator of the signal’s Z-transform Parameter tuning |
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| References_xml | – volume: 36 start-page: 1627 year: 1964 ident: 9875_CR24 publication-title: Anal. Chem. doi: 10.1021/ac60214a047 contributor: fullname: A Savitzky – volume: 7 start-page: 116 year: 1969 ident: 9875_CR21 publication-title: J. Comb. Theor. doi: 10.1016/S0021-9800(69)80045-1 contributor: fullname: BC Rennie – ident: 9875_CR26 doi: 10.1016/j.ijforecast.2006.03.001 – ident: 9875_CR2 doi: 10.3182/20090706-3-FR-2004.00256 – ident: 9875_CR16 – volume-title: Applied Analysis year: 1956 ident: 9875_CR18 contributor: fullname: C Lanczos – ident: 9875_CR4 doi: 10.3182/20090706-3-FR-2004.00239 – ident: 9875_CR10 doi: 10.1109/CDC.2009.5400719 – volume: 45 start-page: 364 year: 1998 ident: 9875_CR23 publication-title: IEEE Trans. Ind. Electron. doi: 10.1109/41.681239 contributor: fullname: S Valiviita – volume: 99 start-page: 403 year: 1992 ident: 9875_CR15 publication-title: Am. Math. Mon. doi: 10.2307/2325085 contributor: fullname: DE Knuth – ident: 9875_CR11 – volume: 50 start-page: 439 issue: 4 year: 2009 ident: 9875_CR5 publication-title: Numer. Algoritm. doi: 10.1007/s11075-008-9236-1 contributor: fullname: M Mboup – volume: 27 start-page: 402 year: 1989 ident: 9875_CR14 publication-title: Fibonacci Quart. contributor: fullname: N Gauthier – ident: 9875_CR27 doi: 10.1504/IJMIC.2008.020996 – volume: 20 start-page: 219 issue: 3 year: 1990 ident: 9875_CR6 publication-title: Signal Process. doi: 10.1016/0165-1684(90)90012-N contributor: fullname: MRR Reddy – ident: 9875_CR8 – volume: 22 start-page: 993 year: 1977 ident: 9875_CR13 publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.1977.1101671 contributor: fullname: D Smith – ident: 9875_CR19 doi: 10.1016/j.crma.2006.02.037 – volume: 34 start-page: 283 issue: 5 year: 2007 ident: 9875_CR20 publication-title: Gaz. Aust. Math. Soc. contributor: fullname: M Nyblom – ident: 9875_CR1 doi: 10.1109/MED.2007.4433728 – ident: 9875_CR28 doi: 10.1109/MED.2010.5547743 – ident: 9875_CR25 – ident: 9875_CR17 – ident: 9875_CR22 doi: 10.1109/CCA.2007.4389252 – ident: 9875_CR3 – volume: E90-A start-page: 1511 issue: 8 year: 2007 ident: 9875_CR9 publication-title: IEICE Trans. doi: 10.1093/ietfec/e90-a.8.1511 contributor: fullname: S Samadi – ident: 9875_CR12 – volume: 35 start-page: 1695 issue: 20 year: 1999 ident: 9875_CR7 publication-title: Electron. Lett. doi: 10.1049/el:19991183 contributor: fullname: G Mollova |
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| Snippet | The seminal work of Mboup et al. [
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| SubjectTerms | 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 |
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| Title | Design of a discrete algebraic robust differentiation FIR filter using an annihilator of the Z-transform; frequency response analysis and parameter tuning |
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