双参数自适应格形滤波器的随机收敛特性

Stochastic Convergence Properties of Two-parameter Adaptive Lattice Filters

本文用矩阵特征值摄动理论、算子谱范数和不动点原理研究了双参数自适应格形滤波器的随机特性。双参数相对差值‖△_(nst)‖是重要的因子。得到如下结论:1.元算子均值的奇值在半径正比于‖△_(nst)‖的圆内变化,‖△_(nst)‖不但改变奇值的大小,还改变它的方向;2.元算子均方值的特征值在半径正比于‖△_(nst)‖的圆内变化;3.步距β_m的取值比单参数的情形更为严格;4.不存在零失调,它在以单参数时的失调为中心,长度正比于‖△_(nst)‖的区间内变化;5.失调与阶数N的关系既不是线性的,也不是指数的,基本上介于两者之间;6.确定性信号的收敛速率慢于不相关信号的速率。

The perturbation theory of matrix characteristic values, the operator spectral norm and a fixed-point theorem has been used to find the stochastic conversence properties of two-parameter adaptive lattice filters. The relative difference value ||Δn,t|| between the two parameters is an important factor. The results are: obtained 1, The singular values of the mean elementary operator may be varied in a circle with the radius proportional to ||Δn,t||, they change not only in the magnitude, but also in the direction due to ||Δn,t||; 2, The characteristic values of the mean square elementary operator may ve varied in a circle whose radius is proportional to ||Δn,t|| also: 3, The limits of stepsize βn are more critical than in the case of one-parameter lattice filters; 4, Zero-misadjustme-nt can not be obtained. The misadjustment varies in the range, where its center is equal to the misadjustment of one-paramenter lattice filters and its length is proportional to ||Δn,t||; 5, The relations between the misadjustment and the order N are neither linrar nor exponential, but are between them basically; 6, The convergence rate of deterministic signal is slower than the one of uncorrelated signal.