Closed Form Approach for Constrained Design of nth-Order IIR Digital Differentiator

被引：0
作者：
Masayoshi Nakamoto
Naoyuki Aikawa
机构：
[1] Hiroshima University,Graduate School of Advanced Science and Engineering
[2] Tokyo University of Science,Department of Applied Electronics
来源：
Circuits, Systems, and Signal Processing | 2023年 / 42卷
关键词：
th-order differentiator; Infinite impulse response (IIR); Closed form cost function; Pole radius constraint; Discrete optimization;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This work presents a new design method for nth-order infinite impulse response (IIR) differentiators. First, the cost function of the IIR differentiator is derived in closed form without frequency sampling. Next, a new optimization scheme is proposed to minimize the cost function under the pole radius constraint. Here, the magnitude and phase specifications are approximated simultaneously with a stability margin. Furthermore, discrete optimization for the IIR differentiator is presented for a specified word length constraint. The discrete optimization results in a stable IIR differentiator with finite word length coefficients owing to the stability margin. Finally, several design examples are demonstrated to evaluate the efficiency of the proposed method.
引用
收藏
页码：3385 / 3411
页数：26
相关论文
共 42 条
  • [1] Ababneh J(2021)Design of approximately linear phase low pass IIR digital differentiator using differential evolution optimization algorithm Circuits Syst. Signal Process. 40 5054-5076
  • [2] Khodier M(2007)Linear phase low-pass IIR digital differentiators IEEE Trans. Signal Process. 55 697-706
  • [3] Al-Alaoui M(2010)Linear programming algorithms for sparse filter design IEEE Trans. Signal Process. 58 1605-1617
  • [4] Baran T(2008)Output feedback controller design for a class of MIMO nonlinear systems using high-order sliding-mode differentiators with application to a laboratory 3-D crane IEEE Trans. Ind. Electron. 55 3985-3997
  • [5] Wei D(1982)A linear programming approach to recursive digital filter design with linear phase IEEE Trans. Circuits Syst. CAS–29 139-149
  • [6] Oppenheim AV(2020)A novel approach for the design of optimum IIR differentiators using fractional interpolation Circuits Syst. Signal Process. 39 1688-1698
  • [7] Chen W(2021)Closed-form analytical formulation for Riemann–Liouville-based fractional-order digital differentiator using fractional sample delay interpolation Circuits Syst. Signal Process. 40 2535-2563
  • [8] Saif M(2011)Robust parameter estimation of nonlinear systems using sliding-mode differentiator observer IEEE Trans. Ind. Electron. 58 680-689
  • [9] Chottera A(2017)Design method for low-delay maximally flat fir digital differentiators with variable stopbands obtained by minimizing IEICE Trans. Fundam. E100–A 1713-1721
  • [10] Jullien G(1976) norm IEEE Trans. Acoust. Speech Signal Process. ASSP–24 226-238
12345