A new state space representation method for adaptive log domain system

Abstract

In this paper, a new method for the state space representation of a system is proposed, which is based on the companion form technique. It is very important to have almost equal coefficients of state space equations since their coefficients are proportional to devices' currents or voltages, e.g. transistors' currents for log domain filters. The method gives us the opportunity to choose two arbitrary parameters (alpha, beta) to be able to obtain more balanced state space equations. This method is applied a log domain filter, which can be considered an adaptive filter since it can be electronically tuned. It is particularly useful for higher order log domain filters synthesized in the state space.