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Design of IIR Digital Filters with Prescribed Phase Error and Reduced Group-delay Error

机译:具有规定相位误差和减小群时延误差的IIR数字滤波器的设计

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Digital filters are often required to have constant group delays in many applications. Existing designs of IIR digital filters with no explicit constraints on the filters’ group-delay responses usually lead to large group-delay errors, especially near the band edges. In design methods with constraints on group-delay error, much reduction of group-delay error have been obtained, but the phase error may not be small enough. In this paper, we design the IIR filter by imposing constraints on its frequency-response error and phase error, and using a sigmoid upper-bound function to shape the phase error. With this method, we have obtained both small phase error and groupdelay error. In order to implement the design method, we combine the Steiglitz-McBride strategy with a relaxation scheme to convert the nonconvex design problem into a series of feasible quadratically constrained quadratic programming problems. Two example filters with specifications given in the literature are provided to compare the proposed design method with several existing methods. Design results demonstrate the effectiveness of the proposed method and good properties of the designed filters.
机译:在许多应用中,通常要求数字滤波器具有恒定的群延迟。现有的IIR数字滤波器设计没有明确限制滤波器的群延迟响应,通常会导致较大的群延迟误差,尤其是在频带边缘附近。在对群时延误差有约束的设计方法中,虽然已大大降低了群时延误差,但是相位误差可能还不够小。在本文中,我们通过对IIR滤波器的频率响应误差和相位误差施加约束,并使用S形上限函数来对相位误差进行整形来设计IIR滤波器。通过这种方法,我们获得了小相位误差和群延迟误差。为了实现设计方法,我们将Steiglitz-McBride策略与松弛方案相结合,将非凸设计问题转换为一系列可行的二次约束二次规划问题。提供了两个在文献中给出规格的示例滤波器,以将建议的设计方法与几种现有方法进行比较。设计结果证明了所提方法的有效性和所设计滤波器的良好性能。

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