Generalized Schwarz form and lattice - ladder realizations of digital filters

This paper deals with the structural properties of lattice-ladder realization of digital filters in a state-space model context. A salient feature of the lattice-ladder realization in state space is its close connection to the Schwarz form, a class of matrices which plays a key role in the stability analysis of linear systems. This connection is further investigated and generalized in this paper to yield a new class of matrices called a generalized Schwarz form. Based on the recursive structure of this new class of matrices, it is shown that there are2^{n}- 1lattice realizations of a given digital filter of ordern, each of which corresponds to a different way of connecting lattice sections. Some interesting algebraic properties of generalized lattice realizations are derived which recast the input/output properties of lattice-ladder form from the state-space point of view. Practical advantages of using the generalized lattice form are discussed and a design example is illustrated.