State-Space Analysis of Power Complementary Filters

Shunsuke KOSHITA  Masahide ABE  Masayuki KAWAMATA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.10   pp.2265-2271
Publication Date: 2007/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.10.2265
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Analog Signal Processing
state-space representation,  power complementary,  controllability Gramian,  observability Gramian,  bounded-real Riccati equation,  

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This paper presents a new analysis of power complementary 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. Through this new state-space analysis of power complementary filters, we prove 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 shows 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. Finally, we give a numerical example to demonstrate our results.