Toward tools and methodology for the fixed-point implementation OF linear filters

For embedded systems, Finite Word Length (FWL) effect is still a critical issue in digital filter implementation with fixed-point arithmetic. Few partial solutions exist, but none tackles it in its global nature and consider the complete tradeoff between performance, precision, complexity and hardware cost. This paper proposes to formalize this complex problem and exhibits a unifying approach for the optimal implementation problem of linear filters/controllers. The proposed methodology is based on previously proposed formal description and measures of the FWL effects. A two steps optimization is proposed and a small example emphasizes the process.