Improved Interval-Based Characterization of Fixed-Point LTI Systems With Feedback Loops

Traditional approaches for fixed-point characterization are based on long simulations or additive noise models that do not show the nonlinear behavior of the quantization operations in reasonable time. In this paper, a novel interval-based approach that provides both tighter and faster results than the existing approaches is presented. It is based on a nonlinear adaptation of the quantization operations of affine arithmetic (AA). The results obtained with this method are compared to other published interval-based approaches, and the problem of interval oversizing is discussed in detail. Simulations show that: 1) the propagation techniques are not well suited to characterize the quantized linear systems with feedback loops; 2) the AA provides oversized bounds in this type of systems; and 3) the proposed adaptation does not provide guaranteed bounds as in the traditional interval-based computations, but it provides tighter estimates of the evolution in time of the ranges of the fixed-point signals and better runtime than the existing interval-based characterization techniques.