Dr. Frey, STATE-SPACE SYNTHESIS AND ANALYSIS OF LOG-DOMAIN FILTERS, IEEE transactions on circuits and systems. 2, Analog and digital signal processing, 45(9), 1998, pp. 1205-1211
The general state-space synthesis of linear filters is reviewed includ
ing the use of linear transformations. Then the use of time-varying no
nlinear 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 formulati
on.