Arbitrary-length filter banks and robust frames: theory and factorization

221 p.Over the past two decades, there have been persistent interests in the study of filter banks (FBs), due to their successes in wide applications such as compression, filtering and communication, and their unifying role for block, lapped and wavelet transforms. The core issue in the study of FBs is the theory and design approaches. Among all the existing methods, one of the most efficient ones is the lattice factorization based design method which employs the classic divide-and-conquer strategy, i.e., constructing a higher-order matrix polynomial by cascading several lower-order modular building blocks. Lattice factorization can offer modular and robust structures which enable the unconstrained optimization based FB design and are friendly to hardware realization in very large scale integrated circuits. Taking account of these advantages, this dissertation is devoted to a systematic investigation of the theory, lattice factorizations and designs for both critically sampled and oversampled FBs, as studied in Part I (Chapters 2-5) and Part II (Chapters 6-8), respectively.DOCTOR OF PHILOSOPHY (EEE