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StateSpace Analysis of Power Complementary Filters
Shunsuke KOSHITA Masahide ABE Masayuki KAWAMATA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E90A
No.10
pp.22652271 Publication Date: 2007/10/01
Online ISSN: 17451337
DOI: 10.1093/ietfec/e90a.10.2265
Print ISSN: 09168508 Type of Manuscript: PAPER Category: Analog Signal Processing Keyword: statespace representation, power complementary, controllability Gramian, observability Gramian, boundedreal Riccati equation,
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Summary:
This paper presents a new analysis of power complementary filters using the statespace representation. Our analysis is based on the boundedreal Riccati equations that were developed in the field of control theory. Through this new statespace 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 boundedreal 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 boundedreal 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.

