State-space synthesis and analysis of log-domain filters

The general state-space synthesis of linear filters is reviewed including the use of linear transformations. Then the use of time-varying nonlinear mappings on the state variables is shown to produce equations for the synthesis of linear, linear companding, and log-domain filters. Formulas are developed which underlie the realization of log-domain filters. Design issues relating to realizability, noise, and nonideal performance are discussed using the state-space mathematical formulation.