Error analysis methods for the fixed-point implementation of linear systems

In this paper we propose to perform a complete error analysis of a fixed-point implementation of any linear system described by data-flow graph. The system is translated to a matrix-based internal representation that is used to determine the analytical errors-to-output relationship. The error induced by the finite precision arithmetic (for each sum-of-product) of the implementation propagates through the system and perturbs the output. The output error is then analysed with three different point of view: classical statistical approach (errors modeled as noises), worst-case approach (errors modeled as intervals) and probability density function. These three approaches allow determining the output error due to the finite precision with respect to its probability to occur and give the designer a complete output error analysis. Finally, our methodology is illustrated with numerical examples.