Synthesis of minimum quantization error digital filters using floating‐point arithmetic

Quantization error arising from roundoff and coefficient quantization presents a serious problem in realizing a digital filter with finite‐word length arithmetic. This paper proposes floating‐point realizations of digital filters that minimize quantization error. A filter synthesis problem is formulated with the relationship between round‐off error and coefficient quantization error that has recently been investigated by the authors. the formulation reveals that a combination of the minimum‐ coefficient‐sensitivity structure and the optimum order of additions leads to a realization of a digital filter with the minimum quantization noise. the proposed synthesis consists of transformations in a state space. the optimum ordering of additions is found with the assumption of the use of the successive addition that is amiable to hardware implementation. Finally, the effectiveness of the proposed method is illustrated by an example.