A Matrix Factorization-Based Structure for Digital Filters
Gang Li, Jian Chu, Jun Wu · IEEE Transactions on Signal Processing · 2007
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 [ldquoPerformance Analysis of a New Structure for Digital Filter Implementation,rdquo IEEE Transactions on Circuits and Systems I, vol. 47, no. 4, pp. 474-482, April 2000]. For a digital filter of order , 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.