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Linear phase filter bank design by convex programming

Digital filter banks have found in a wide variety of applications in data compression, digital communications, and adaptive signal processing. The common objectives of the filter bank design consist of frequency selectivity of the individual filters and perfect reconstruction of the filter banks. The design problems of filter banks are intrinsically challenging because their natural formulations are nonconvex constrained optimization problems. Therefore, there is a strong motivation to cast the design problems into convex optimization problems whose globally optimal solutions can be efficiently obtained. The main contributions of this dissertation are to exploit the convex optimization algorithms to design several classes of the filter banks. First, the two-channel orthogonal symmetric complex-valued filter banks are investigated. A key contribution is to derive the necessary and sufficient condition for the existence of complex-valued symmetric spectral factors. Moreover, this condition can be expressed as linear matrix inequalities (LMIs), and hence semi-definite programming (SDP) is applicable. Secondly, for two-channel symmetric real-valued filter banks, a more general and efficient method for designing the optimal triplet halfband filter banks with regularity is developed. By exploiting the LMI characterization of nonnegative cosine polynomials, the semi-infinite constraints can be efficiently handled. Consequently, the filter bank design is cast as an SDP problem. Furthermore, it is demonstrated that the resulting filter banks are applied to image coding with improved performance. It is not straightforward to extend the proposed design methods for two-channel filter banks to M-channel filter banks. However, it is investigated that the design problem of M-channel cosine-modulated filter banks is a nonconvex optimization problem with the low degree of nonconvexity. Therefore, the efficient semidefinite relaxation technique is proposed to design optimal prototype filters. Additionally, a cheap iterative algorithm is developed to further improve the performance of the filter banks. Finally, the application of filter banks to multicarrier systems is considered. The condition on the transmit filter bank and channel for the existence of zero-forcing filter bank equalizers is obtained. A closed-form expression of the optimal equalizer is then derived. The proposed filter bank transceivers are shown to outperform the orthogonal frequency-division multiplexing (OFDM) systems.
Date January 2008
CreatorsHa, Hoang Kha, Electrical Engineering & Telecommunications, Faculty of Engineering, UNSW
PublisherPublisher:University of New South Wales. Electrical Engineering & Telecommunications
Source SetsAustraliasian Digital Theses Program
Detected LanguageEnglish

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