Reliable Fixed-Point Implementation of Linear Data-Flows

In this article, we propose a complete methodology to implement a signal processing or control-engineering algorithm described with a linear data-flow into numerical code using fixed-point arithmetic. Our approach is based on a reliable determination of the Worst-Case Peak gain of a filter as well as on rigorous error analysis of roundoff error propagation. It guarantees that no overflow will occur and that the output error due to the finite precision implementation is less than a given bound. Without loss of generality, we consider the linear data-flows given in the form of Simulink block diagram. It is first transposed into an internal matrix-based representation and then the reliable evaluation of the magnitudes of each internal variable is performed. Our approach allows determining the minimum word-length required to achieve a given accuracy. Finally, the methodology is illustrated with numerical examples.