Reliable implementation of linear filters with fixed-point arithmetic

This article deals with the implementation of linear filters or controllers with fixed-point arithmetic. The finite precision of the computations and the roundoff errors induced may have an important impact on the numerical behavior of the implemented system. More-over, the fixed-point transformation is a time consuming and error-prone task, specially with the objective of minimizing the quantization impact. Based on a formalism able to describe every structure of linear filters/controllers, this paper proposes an automatic method to generate fixed-point version of the inputs-to-outputs algorithm and an analysis of the global error added on the output. An example illustrates the approach.