STOCHASTIC CONVERGENCE PROPERTIES OF THE TWO-PARAMETER ADAPTIVE LATTICE FILTERS

In this paper,the perturbation theory of the matrix eigenvalues,the operator spectral norm and a fixed-point theorem are used to research on the stochastic convergence properties of the two-parameter adaptivelattice filters.The relative difference value between the two parameters is a important factor.We obtainsome results:1.The singular values of the mean of elementary operator vary in a circle which has the radiusproportionated to ,they vary not only in magnitude,but also in direction due to; 2.Theeigenvalues of the mean square of elementary operator vary in a circle,its radius is proportional to also;3.The limits of stepsize are stricker than the ones of the one-parameter lattice filters;4.Zero-misadjustment can not be obtained.The misadjustment varys in the range where the center is equal to themisadjustment of the one-parameter lattice filters and the length is propertional to 5.The relationsbetween the misadjustment and order Nare neither linear nor exponential,but are in some conditions betweenthe