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

Among the best structures for implementing recursive digital filters are lattice wave digital (LWD) filters (parallel connections of two all-pass 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 representations. In order to get around this problem, a structure consisting of a cascade of LWD filters is introduced in this paper. The main advantage of the proposed structure, compared with the direct LWD filter, is that the poles of the new structure are further away from the unit circle. Consequently, the number of bits required for both the data and coefficient representations are significantly reduced. The price paid for these reductions is a slight increase in the overall filter order. By properly selecting the number of LWD filters and their orders and optimizing them, their coefficients are implementable by using a few powers of two. Filters of this kind are very attractive in very large-scale integration (VLSI) implementations, where a general multiplier is very costly.