IIR数字滤波器的序列约束Chebyshev设计方法

A Sequential Constrained Chebyshev Design Method of IIR Digital Filters

进行无限冲击响应(IIR)数字滤波器的无约束Chebyshev设计时,得到的滤波器幅值响应通常在过渡带存在明显过冲现象,且通带边缘的群延迟误差较大。本文提出一种序列约束Chebyshev(SCC)方法,在通带和阻带最大频率响应(FR)误差小于某给定值ρ的条件下,使过渡带频率响应误差(相对某个具有单调幅值特性的过渡响应函数)的Cheby-shev模最小,并通过收缩和对分找出ρ的最小值。该方法不但可以使通带和阻带最大频率响应误差尽可能小,还能减小过渡带幅值响应的过冲以及带边群延迟误差。仿真实例表明了该方法的有效性。

The magnitude response of unconstrained Chebyshev infinite impulse response （IIR） digital filters usually demon- strates an obvious overshoot in the transition band and large group-delay error near the passband edge. This paper presents a sequential constrained Chebyshev （SCC） method that formulates the design as a series of constrained Chebyshev problems by minimizing the Chebyshev norm of the error between the transition-band frequency response （FR） and a preset monotoni- cally increasing/decreasing transient function subject to a constraint that the maximum magnitude of the passband and stop- band FR error is smaller than a given value p, the minimum value of which is obtained by a shrinking followed by bisection search. The SCC method can not only render as small as possible the maximum magnitude of the passband and stopband FR error, but also reduce obviously the magnitude overshoot on the transition band and the group-delay error near the passband edge. Simulation results demonstrate the effectiveness of the proposed method.