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 IBRbased 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 Rnew, which is in fact an improved version of the structure Rlgs proposed in [8]. The second one is to analyze the roundoff noise behavior of four IBR-based structures, i.e., R
lgs
, 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 Rnl. As to R
new
, it is more general than R
vmn
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 R
lgs
.