Precision analysis with analytical bit‐width optimisation process for linear circuits with feedbacks

Abstract

Finding the best possible word length to accuracy trade off seems to be an obvious design task. However, the literature and carful design reviews show that word lengths are often overestimated to put the data accuracy at the safe side. This study proposes a mathematical process to balance that trade off. It describes an analytical optimisation technique that considers every interconnection and it shows clear improvement with respect to published results. To allow reproducibility of their work, detailed procedures are provided. Implementation results are presented for different configurations of infinite impulse response filters. More, the impact of the proposed bit-width optimisation on the filter poles and zeros is provided to show the effectiveness of the proposed solution. Their solution provides overall improvement going up to 17% of the circuit's area with respect to existing methods. The proposed technique for uniform fractional bits allocation runs in a negligible time independently of the targeted accuracy.