Sum-of-products Evaluation Schemes with Fixed-Point arithmetic, and their application to IIR filter implementation

Benoit Lopez (1) , Thibault Hilaire (1) , Laurent-Stéphane Didier (1)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques

— The signal processing and control algorithms are widely based on sum-of-products evaluation. In fixed-point arith-metic, the roundoff errors and coefficient quantization may have an important effect on the application's performance and characteristics. As part of a global methodology on optimal fixed-point im-plementation of filters/controllers, this paper formalizes the various implementation schemes for sum-of-products in fixed-point arithmetic and automates the fixed-point code production. The order of the operations are considered, as their bit-width and the fixed-point representation of the coefficients, variables and partial results. Applied to linear filters, the output roundoff noise error is then evaluated and used as a criteria to find out interesting evaluation scheme. An example illustrates the approach.

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

Benoit Lopez, Thibault Hilaire, Laurent-Stéphane Didier. Sum-of-products Evaluation Schemes with Fixed-Point arithmetic, and their application to IIR filter implementation. Conference on Design and Architectures for Signal and Image Processing (DASIP), Oct 2012, Karlsruhe, Germany. ⟨hal-01076043⟩