Optimal Word-Length Allocation for the Fixed-Point Implementation of Linear Filters and Controllers

Thibault Hilaire (1, 2) , Hacène Ouzia (3) , Benoit Lopez (2)

1 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations
2 PEQUAN - Performance et Qualité des Algorithmes Numériques
3 DECISION

This article presents a word-length optimization problem under accuracy constraints for the hardware implementation of linear signal processing systems with fixed-point arithmetic. For State-Space systems (describing a linear filter or a controller), a complete error analysis is exhibited, where the final output error bound depends on the word-lengths and the fixed-point formats chosen for each variable. The Most Significant Bit of each one can be determined in order to guarantee that no overflow occurs. Thus, it is possible to obtain a hardware implementation minimizing resource use. This leads to a convex nonlinear integer optimization problem where the resources to minimize and the accuracy constraints depend on the internal word-lengths. This problem can then be solved with appropriate heuristics. Finally, a global approach is proposed and illustrated by some examples.

Mots clés: fixed-point arithmetic; word-length allocation

Domaines: Arithmétique des ordinateurs; Traitement du signal et de l'image [eess.SP]; Optimisation et contrôle [math.OC]

Thibault Hilaire, Hacène Ouzia, Benoit Lopez. Optimal Word-Length Allocation for the Fixed-Point Implementation of Linear Filters and Controllers. ARITH 2019 - IEEE 26th Symposium on Computer Arithmetic, Jun 2019, Kyoto, Japan. pp.175-182, ⟨10.1109/ARITH.2019.00040⟩. ⟨hal-02393851⟩