ABSTRACT A new approach to the design of the nearly linear phase infinite impulse response low-pass differentiators using a parallel all-pass structure is discussed in this paper. The magnitude and phase responses of the proposed low-pass differentiators are first formulated as functions of the phase responses of the corresponding all-pass filters, and a set of equations is derived such that the magnitude response approximates the ideal one in the weighted Chebyshev sense both in the passband and the stopband. The maximum passband phase response linearity error is shown to be related to the maximum passband magnitude error and the value of an additional design parameter. Comparison with the existing nearly-linear phase infinite impulse response low-pass differentiators shows that the low-pass differentiators designed using the proposed method usually require less multiplications, which comes at the cost of a somewhat higher filter order and consequently higher group delay. However, as the reduced number of multiplications lead to lower power consumption if hardware implementation is considered, the proposed low-pass differentiators are an attractive alternative in applications where low group delay is not of crucial importance.

中文翻译：

---

基于全通的近线性相位 IIR 低通微分器设计

摘要 本文讨论了一种使用并行全通结构设计近线性相位无限脉冲响应低通微分器的新方法。所提出的低通微分器的幅度和相位响应首先被公式化为相应全通滤波器的相位响应的函数，并推导出一组方程，使得幅度响应接近加权切比雪夫意义上的理想值在通带和阻带中。最大通带相位响应线性误差与最大通带幅度误差和附加设计参数的值有关。与现有的近线性相位无限脉冲响应低通微分器的比较表明，使用所提出的方法设计的低通微分器通常需要较少的乘法，这是以更高的滤波器阶数和更高的群延迟为代价的。然而，由于如果考虑硬件实现，乘法次数的减少会导致更低的功耗，因此所提出的低通微分器在低群延迟不是至关重要的应用中是一种有吸引力的替代方案。