Frequency-selective KYP lemma, IIR filter, and filter bank design

Authors:
Hung Gia Hoang;Hoang Duong Tuan;Truong Q. Nguyen
Affiliations:
School of Electrical Engineering and Telecommunication, University of New South Wales, Sydney, NSW, Australia;School of Electrical Engineering and Telecommunication, University of New South Wales, Sydney, NSW, Australia;Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

For a transfer function F(eJω) of order n, Kalman-Yakubovich-Popov (KYP) lemma characterizes a general intractable semi-infinite programming (SIP) condition by a tractable semidefinite programming (SDP) for the entire frequency range. Some recent results generalize this lemma for a certain frequency interval. All these SDP characterizations are given at the expense of the introduced Lyapunov matrix variable of dimension n × n. Consequently, formulation and design of high dimensional problem is challenging. Moreover, existing SDP characterizations for frequency-selective SIP (FS-SIP) do not allow to formulate synthesis problems as SDPs. In this paper, we propose a completely new SDP characterization of general FS-SIP involving SDPs of moderate size and free from Lyapunov variables. Furthermore, a systematic IIR filter and filter bank design is developed in a similar vein, with several simulations provided to validate the effectiveness of our SDP formulation.