A Matrix Factorization-Based Structure for Digital Filters

In this correspondence, a novel digital filter structure is derived using matrix factorization. This structure, called the LCW-structure, is an improved version of the so-called LGS-structure proposed by Li, Gevers, and Sun [“Performance Analysis of a New Structure for Digital Filter Implementation,” IEEE Transactions on Circuits and Systems I , vol. 47, no. 4, pp. 474–482, April 2000]. For a digital filter of order $N$ , this new structure requires $4N-1$ multiplications and $4N-1$ additions for computing one filter output sample, instead of $7N-3$ and $6N-3$, respectively, which are needed for the LGS-structure. An expression of the roundoff noise gain is derived for the LCW-structure. Design examples are presented to demonstrate the behavior of this structure and to compare with several well-known digital filter structures in terms of minimizing roundoff noise and implementation efficiency.