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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。
In this paper, the stochastic character of two-parameter adaptive lattice filter is studied by matrix eigenvalue perturbation theory, operator spectral norm and fixed point principle. The two-parameter relative difference ‖ △ _ (nst) ‖ is an important factor. We get the following conclusions: 1. The odd value of the mean of the element operator changes in a circle whose radius is proportional to ‖ △ _ (nst) ‖, which not only changes the size of the odd value but also changes its direction; 2 The eigenvalue of the mean square value of the element operator changes within a circle whose radius is proportional to ‖ △ _ (nst) ∥, the value of step β_m is more strict than the one parameter, and 4. There is no zero offset, It is in a single parameter imbalance as the center, the length is proportional to ‖ Δ_ (nst) ‖ range of changes; 5 offset and the order N is neither linear nor exponential, basically between two 6. The convergence rate of deterministic signal is slower than that of uncorrelated signal.