Moqbel Mohammed Ali Mohammed, Ali Talal Ahmed Ali, Xiao Zhu
College of Computer Science and Electronic Engineering, Hunan University, Changsha, China.
Shenzhen Research Institute, Hunan University, Shenzhen, China.
PeerJ Comput Sci. 2024 Oct 14;10:e2341. doi: 10.7717/peerj-cs.2341. eCollection 2024.
In this paper, we propose a novel optimization approach to designing wideband infinite impulse response (IIR) digital fractional order differentiators (DFODs) with improved accuracy at low frequency bands. In the new method, the objective function is formulated as an optimization problem with two tuning parameters to control the error distribution over frequencies. The gradient based optimizer (GBO) is effectively employed on the proposed objective function. A wide range of design examples are presented to illustrate the effectiveness of the proposed approach. The proposed approximations are compared to those of recent literature in terms magnitude, phase, and group delay errors. The result reveal that our method can attain approximations have a favorable low frequency performance (with about 60% of relative magnitude error reduction) and maintain a comparable accuracy at most of the Nyquist band to those of the existing ones. Thus, our approximations can be attractive for low frequency applications.
在本文中，我们提出了一种新颖的优化方法，用于设计宽带无限脉冲响应（IIR）数字分数阶微分器（DFOD），以提高其在低频段的精度。在新方法中，目标函数被表述为一个具有两个调谐参数的优化问题，用于控制频率上的误差分布。基于梯度的优化器（GBO）被有效地应用于所提出的目标函数。给出了大量设计示例以说明所提方法的有效性。在所提近似方法与近期文献中的方法之间，在幅度、相位和群延迟误差方面进行了比较。结果表明，我们的方法能够获得具有良好低频性能的近似结果（相对幅度误差降低约60%），并且在奈奎斯特频段的大部分区域与现有方法保持相当的精度。因此，我们的近似方法对于低频应用可能具有吸引力。
