A novel efficient and accurate analytical method for determining the swing of internal nodes in digital filters

Abstract

To implement a floating point system using fixed point representation, it is needed to determine the swing and resolution. In the fixed point representation, swing determines the Integer Bit (IB) and resolution determines the Fraction Bit. Methods for estimation of swing in systems can be divided in to three main categories; analytical methods, simulation-based methods, and semi-analytical methods. Simulation-based methods estimate swing of internal nodes by running a lot of simulations for large amount of inputs. These methods are slow and inaccurate. Interval Arithmetic (IA), Affine Arithmetic (AA), Multi Interval Arithmetic (MIA) and Jackson formula are examples of analytical methods. In these methods, by using mathematical calculations, intervals of signal changes are determined regardless of inputs. These methods usually are fast and accurate, but they are not optimum and the results are overestimated.