The Normal Lattice-A Cascade Digital Filter Structure

A normal lattice is defined as a cascade of two-input two-output second-order normal form digital filter modules. An analysis of this structure is presented along with an iterative algorithm for constructing the system eigenvectors, a scaling algorithm, and an explicit expression for roundoff noise gain. These expressions and algorithms provide an explicit design procedure for realizing arbitrary rational transfer functions for single-input single-output filters. Comparisons with other digital filter structures show that the normal lattice has very low roundoff noise and low coefficient sensitivity in realizations of narrow-band filters. This structure is also well adapted to the realization of complex filters.