Minimum Round-Off Noise Second-Order Digital Filter with Practical Complexity Constraints

Abstract

It is known that, for a specified second-order digital filter transfer function, various realizations with finite precision arithmetic can yield significantly different round-off noises. For high performance communication and radar signal processing applications, the need for low round-off noise is clear. The minimum round-off noise n-th order digital filter of Mullis-Roberts generally requires (n+1)² multipliers. Most practical systems, however, desire to use a low number of multipliers. In this paper, we consider the minimum roundoff noise second-order digital filter realization under the practical complexity constraints of using only four multipliers, two delays, and four two-input adders, The optimum constraint filter has the same complexity as the know canonic direct-form realization, yet its roundoff noise can be significantly smaller for low-frequency rejection filtering applications. Some numerical results are presented.