具有低群延迟的无限冲激长响应数字滤波器优化设计迭代算法

Iterative optimization algorithm of infinite impulse response digital filters' design with low group-delay

针对具有近似线性相位的无限冲激长响应数字滤波器通带边缘附近具有较大群延迟误差情况,提出了一种改进的具有低群延迟约束优化迭代算法。该算法在群延迟约束条件下,通过给定初始值,经过多次迭代优化,得到一个最小化的群延迟。设计要求均满足系统稳定性和最大通带波纹和最小阻带衰减,结合二阶节滤波器结构,为防止过渡带过冲,将过渡带带宽增益控制在1的范围内。最后仿真实验以10阶和18阶的低通无限冲激长滤波器为例,在最大通带波纹为0.266 d B和0.232 d B,最小阻带衰减为36.132 d B和49.97 d B的参数下,用该文算法得到的群延迟与文献中方法相比较,分别降低了32.2%和26%,而过渡带增益了相对降低了10.5%和17.6%。

An improved iterative optimization algorithm（IIOA） is proposed to reduce the large group delay of bandpass for infinite impulse response （IIR） digital filters with nearly linear-phase. When initial group delay values are fixed the group-delay is minimized by the IIOA mentioned here with constraining the maximum passband ripple and minimax stopband attenuation. The second-order sections of filter are described by a set of linear inequality which is used in optimization algorithm. To avoid the abnormal transition band, the scale is set 1. In the experiment the 10-order and 18-order IIR low-pass filters are designed with the 0. 266 dB and 0.232 dB maximum passband ripple and 36. 152 dB and 49.97 dB, minimum stopband attenuation respectively. The experimental results show the group delay obtained here are decreased by 32.2% and 26% through this algorithm compared with the literature method. At the same time transition band gains are decreased by 10.5% and 17.6%.