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Least square design of complex finite impulse response filter
with elliptic error constraint |
| ZHANG Shao-wei2, XU Dong1, YUAN Bo1, LAI Xiao-ping1,2 |
1. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China;
2. School of Information Engineering, Shandong University at Weihai, Weihai 264209, China |
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Abstract A frequency response error and phase error constrained least square method was proposed for the optimal design of nonlinear phase finite impulse response (FIR) filter. The method can control the magnitude error and the phase error independently, and results in the convex feasible domain. By using the sigmoid phaseerror upperbound function, the phase error was controlled within the specified value, and the groupdelay error was greatly reduced, but the magnitude error generally increased. The elliptic complexerror constraints were introduced to constrain the complex frequency response of the filter in order to decrease the magnitude error. Then the weighted least square design of the complex FIR filter was considered with the elliptic complexerror canstraints and the sigmoid phaseerror upper bound. Simulation results show that the magnitude error can be effectively reduced.
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Published: 01 July 2010
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复数FIR滤波器椭圆误差约束最小二乘设计
针对非线性相位有限冲击响应(FIR)滤波器的优化设计问题,提出一种频率响应误差和相位误差约束的最小二乘方法,既能独立控制幅值误差和相位误差,又能形成凸的约束区域.采用S形相位误差上界函数,不仅将相位误差控制在给定范围,而且有效减小了滤波器的群延迟误差,但增大了幅值逼近误差.为了减小幅值逼近误差,应用椭圆形的复数误差约束来代替通带上的圆形频率响应误差约束,研究基于椭圆复数误差约束及S形相位误差上界函数的复系数FIR滤波器加权最小二乘设计.仿真结果表明,应用椭圆形的复数误差约束能够有效减小滤波器的幅值逼近误差.
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