A Generalized Lattice Filter for Finite Wordlength Implementation With Reduced Number of Multipliers

Abstract

The excellent finite wordlength (FWL) property of lattice digital filters is well known. The four-multiplier normalized lattice, with signal power at all delay elements normalized to unity, has particular advantage in its overflow property. However, when used to implement an Nth-order digital filter, the normalized lattice implementation requires 5N+1 multipliers. There exists another lattice structure with excellent FWL property called the injected numerator lattice structure. In this paper, we combine the injected numerator lattice and tapped numerator lattice to form a new hybrid lattice structure, which is not only canonic in the number of multipliers resulting in a significant reduction in overall implementation cost but also exhibits much better FWL properties than the normalized lattice structure. An improved “peakedness” measure is also introduced for application where the input signal has a strong time varying sinusoidal component. The new structure requires a few additional adders; it can be used to implement any causal and stable z-transform transfer function. Two numerical examples are presented to demonstrate the performance of the proposed structure.