Performance characteristics of a third order adaptive Volterra filter

Examines the stability and convergence properties of third order adaptive Volterra filters. The authors consider two forms: a full polynomial implementation, and a reduced complexity implementation, with a significantly lower computational requirement. In both cases, it is shown that for input signals with samples drawn from symmetric densities, the mean convergence proceeds independently for the even and odd order terms of the polynomial expansion. For independent identically distributed (i.i.d.) Gaussian inputs the eigenvalue structure of the corresponding correlation matrices is investigated, and it is shown that the even and odd components differ significantly. This leads to distinct stability limits for the even and odd components of the adaptive filter. As a consequence of the eigenvalue disparity, these third order adaptive Volterra filters suffer from nonuniform convergence even when supplied with i.i.d. inputs