Frequency selective KYP lemma and its applications to IIR filter bank design

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Conference Proceeding
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 2007, 3
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For a transfer function/filter F(εω) of order n, Kalman-Yakubovich-Popov (KYP) lemma characterizes the intractable semi-infinite programming (SIP) condition F(εω)1 ⊖(ε ω)T ≥ 0 V ω in frequency domain by a tractable semi-definite programming (SDP) in state-space domain. Some recent results generalize this lemma to SDP for SIP of frequency selectivity(FS-SIP). All these SDP characterizations are given at the expense of the introduced Lyapunov matrix variable of dimension n × n, making them impractical for high order problem. Moreover, the existing SDP characterizations for FS-SIP do not allow to formulate synthesis/design problems as SDPs. In this paper, we propose a completely new SDP characterization of general FS-SIP, which is of moderate size and is free from Lyapunov variables. Extensive examples are provided to validate the effectiveness of our result. © 2007 IEEE.
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