Design of very low-sensitivity and low-noise recursive digital filters using a cascade of low-order wave lattice filters

Abstract

One of the best structures for implementing recursive digital filters are the wave lattice filters (parallel connections of two allpass filters). They are characterized by many attractive properties, such as a reasonably low coefficient sensitivity, a low roundoff noise level, and the absence of parasitic oscillations. The main drawback is that if the stopband attenuation is very high, then many bits are required for the coefficient representation. In order to get around this problem, a structure consisting of a cascade of wave lattice filters is introduced in this paper. The main advantage of the proposed structure compared to the direct wave lattice filter is that the poles for the new structure are further away from the unit circle. This means that the number of bits required for the data and coefficient representations are significantly reduced compared to the direct wave lattice filters. The price paid for these reductions is a slight increase in the overall filter order. By properly selecting the number of wave lattice filters and optimizing them, their coefficients can be implemented by a few powers-of-two. Filters of this kind are very attractive in VLSI implementations where a general multiplier is very costly.