Comparative study of input-balanced realization-based digital filter structures

Input-balanced realizations (IBR) are a very important class of digital filter representations. In this paper, four IBR- based digital filter structures are compared in terms of roundoff noise behavior. Our main contribution is twofold. The first one is to derive a novel digital filter structure, denoted as R_new, which is in fact an improved version of the structure Rl_gs proposed in [8]. The second one is to analyze the roundoff noise behavior of four IBR-based structures, i.e., Rl_gs, R_new, the famous normalized lattice structure R_nl [5] , and the one (denoted as R_vmn) proposed in [6]. The expression of roundoff noise gain for each structure is derived. It is shown that a filter yields a smaller roundoff noise gain when implemented with R_vmn than with R_nl. As to R_new, it is more general than Rvmn and the most efficient among the four in terms of number of multiplications needed for computing one filter output sample. Design examples show that the roundoff noise gain of R_new is almost the same as that of R_vmn and much smaller than R_nl and Rl_gs.