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Iterative Reweighted Minimax Phase Error Designs of IIR Digital Filters With Nearly Linear Phases

机译:具有近似线性相位的IIR数字滤波器的迭代加权最小最大相位误差设计

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摘要

Linear phase is an important characteristic of digital filters in many signal processing applications. In this paper, two iterative reweighted minimax phase error algorithms are proposed to design nearly linear-phase infinite impulse response (IIR) digital filters with prescribed or simultaneously minimized magnitude errors and preset transition-band gain. In each iteration of the algorithms, a weighted minimax phase error problem with a fixed weight function is firstly solved using a modified Gauss-Newton method with a variable step length, and the weight function of the phase error is then updated using the square root of a modified envelope of the group-delay error of the filter. With the proposed methods, both very small phase error and group-delay error have been obtained while meeting the requirements on the passband and stopband magnitude errors and the transition-band gain. Design examples demonstrate the effectiveness of the proposed methods and the excellent performance of the designed filters.
机译:线性相位是许多信号处理应用中数字滤波器的重要特征。本文提出了两种迭代的加权最小最大相位误差算法,以设计具有规定或同时最小化幅度误差和预设过渡带增益的近线性相位无限脉冲响应(IIR)数字滤波器。在算法的每次迭代中,首先使用具有可变步长的改进的Gauss-Newton方法求解具有固定权函数的加权minimax相位误差问题,然后使用的平方根更新相位误差的权函数。滤波器的群时延误差的修改包络。利用所提出的方法,在满足通带和阻带幅度误差以及过渡带增益的要求的同时,已经获得了非常小的相位误差和群时延误差。设计实例证明了所提出方法的有效性以及所设计滤波器的出色性能。

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