Very Robust Low Complexity Lattice Filters

In this paper, a novel lattice filter structure is derived by combining the “tapped numerator” and “injected numerator” lattices [Y. C. Lim, “On the Synthesis of IIR Digital Filters Derived From Single Channel AR Lattice Network,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-32, no. 4, pp. 741-749, August 1984]. The injector coefficients are optimized for finite wordlength performance while the tapped coefficients synthesize the transfer function of the filters. For an
N
th-order digital filter, the proposed “tapped numerator” and “injected numerator” hybrid lattice structure, after optimization, has only 2
N
+1 multipliers. It is not only canonic in the number of multipliers but also possesses much improved finite wordlength properties such as very low parameter sensitivity and very uniform signal powers across signal nodes. The excellent finite wordlength performance of the proposed structure is demonstrated with a design example and compared with those of traditional structures, including several well-known lattice structures.