Interrelations between continuous and discrete lattice filter structures

The authors explore the connection between continuous and discrete lattice filtering algorithms. Lattice filters become ill-defined when applied to continuous-time processes sampled at very fast rates. It is shown that these problems are resolved if the standard formulation of lattice filter structures, based on the forward shift operator, is replaced by an alternative formulation based on the incremental difference (or delta) operator. The lattice algorithms corresponding to the continuous and discrete cases are presented in a unified framework, thereby revealing their common structure. It is shown that when the discrete problem is obtained by sampling an underlying continuous time system, then the lattice filter corresponding to the discrete case converges in a well defined sense to the solution of the underlying continuous problem as the sampling period approaches zero