设计稳定约束最小二乘无限冲击响应滤波器的序列最小化方法

A sequential minimization procedure for constrained least-squares design of stable infinite impulse response filters

中文关键词  无限冲击响应数字滤波器  约束最小二乘设计  稳定三角形  序列最小化

英文关键词  IIR digital filters  constrained least-squares design  stability triangle  sequential minimization

中文摘要

      无限冲击响应(infinite impulse response, IIR)数字滤波器不具有内禀稳定性, 因此在其实际设计中要施加稳定性约束. 稳定三角形条件是一种充分必要且线性的稳定性约束条件, 为了充分利用该条件, 本文使用基于二阶因子迭代更新的序列最小化技术将IIR滤波器的约束最小二乘设计问题转化为一系列的约束最小二乘子问题, 在每一个子问题中, 有且只有一个二阶分母因子连同整个分子被优化, 其他的二阶分母因子保持不变. 设计实例表明此方法能比现有方法得到性能更好的滤波器.

英文摘要

      Infinite impulse response (IIR) digital filters do not have intrinsic stability; thus, stability constraints should be imposed on their practical designs. The stability-triangle is a necessary-sufficient linear stability condition for IIR digital filters. In order to make good use of the stability-triangle condition, a sequential minimization procedure based on secondorder factor is employed to convert the constrained least-squares design of IIR digital filters into a sequence of constrained least-squares sub-problems, each of which optimizes only one second-order denominator factor while keeping all the rest denominator factors unchanged. Design examples show that the proposed procedure provides better filtering performances than other existing methods.