In this paper, the design of nearly linear-phase recursive digital filters using a constrained optimization method is investigated. The method is based on existing constrained optimization techniques for nearly linear-phase IIR digital filters, and it is expected to be useful in applications where both magnitude and phase response specifications are required to be satisfied. Starting from an initial filter, the proposed method minimizes the group delay deviation under a set of linear constraints in terms of the magnitude response and filter stability. Improved sampling functions are introduced to the optimization problem, which are used to control the sampling points that are used for approximating the group delay and the rest of the constraints in various frequency bands. By using the proposed sampling functions we get an improved IIR filter response.

中文翻译：

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使用约束优化改进近线性相位 IIR 滤波器的设计方法

在本文中，研究了使用约束优化方法的近线性相位递归数字滤波器的设计。该方法基于现有的近线性相位 IIR 数字滤波器的约束优化技术，预计可用于需要满足幅度和相位响应规范的应用。从初始滤波器开始，所提出的方法在幅度响应和滤波器稳定性方面最小化一组线性约束下的群延迟偏差。改进的采样函数被引入到优化问题中，用于控制用于逼近群延迟的采样点和不同频段的其余约束。