LATTICE FILTRATION THEORY. PART I: ONE-DIMENSIONAL LATTICE FILTERS

Abstract

We address the role and place of lattice filters (LF) in systems of primary space-time signal processing, the state-of-the-art of the LF theory and adaptive adjustment techniques. The first part deals with the development of a unified technique for synthesis of multistage fil-ters with given matrix impulse responses based on their factorized representations of vari-ous types. The generalized Levinson algorithm and the generalized Levinson factorization, being theoretical grounds for the lattice structures, are derived. A physical meaning and properties of parameters of whitening and inverse LFs are discussed, given different levels of a priori information about the input signals’ covariance matrix specificity.