State-Space Analysis of Power Complementary Analog Filters

This paper presents a new analysis of power complementary analog filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. We show that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result means that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems.