Some properties of lattice autoregressive filters

An autoregressive filter is defined either by the components of the regression vector or by the reflection coefficients appearing in its lattice representation. The mathematical expression of the regression vector in terms of the reflection coefficients is very complex but many structural properties can be obtained without this exact expression. In this paper, we present some examples of such structural properties, and we apply these results to prove some extremal properties of stable filters such as the maximum value of the components of the regression vector or the maximum value of its norm. Moreover, some properties of the boundary of the stability domain are discussed.