This thesis investigates several design problems concerning two-channel conjugate quadrature (CQ) filter banks and orthogonal wavelets, as well as orthogonal cosine-modulated (OCM) filter banks. It is well known that optimal design of CQ filters and wavelets and optimal design of prototype filters (PFs) of OCM filter banks in the least squares (LS) or minimax sense are nonconvex problems and to date only local solutions can be claimed. In this thesis, we first make some improvements over several direct design techniques for local design problems in terms of convergence and solution accuracy. By virtue of the recent progress in global polynomial optimization and the improved local design methods mentioned above, we describe an attempt at developing several design strategies that may be viewed as our endeavors towards global solutions for LS CQ filter banks, minimax CQ filter banks, and OCM filter banks. In brief terms, the proposed design strategies are based on several observations made among globally optimal impulse responses of low-order filter banks, and are essentially order-recursive algorithms in terms of filter length combined with some techniques in identifying a desirable initial point in each round of iteration. This main idea is applied to three design scenarios in this thesis, namely, LS design of orthogonal filter banks and wavelets, minimax design of orthogonal filter banks and wavelets, and design of orthogonal cosine-modulated filter banks. Simulation studies are presented to evaluate and compare the performance of the proposed design methods with several well established algorithms in the literature.

This study deploys the decolonial epistemic perspective in an attempt to unmask the spectre of xenophobia. The decolonial epistemic thinking is in turn predicated on three important concepts, namely coloniality of power, coloniality of being and coloniality of knowledge. The study is focused on understanding the dynamics of the violent May 2008 attacks that took place in Alexandra and Yeoville. It problematised the use of the term xenophobia. The term occludes rather than enlightening the complex phenomenon of violence. Such violence has consistently and systematically engulfed people living in poor predominantly black areas of residence such as Yeoville and Alexandra. The study also used empirical evidence collected from the field to support its central arguments. What has been understood as xenophobia is in actual fact, part of the manifestation and outcome of abject living conditions of the poor. This study argues that what manifests itself as xenophobia is an additional element to various forms of violence taking place in locales such as Alexandra and Yeoville, places that decolonial theorists term ‘zones of non-being,’ where violent death is a constitutive part of human existence. / Development Studies / M.A. (Development Studies)

This study deploys the decolonial epistemic perspective in an attempt to unmask the spectre of xenophobia. The decolonial epistemic thinking is in turn predicated on three important concepts, namely coloniality of power, coloniality of being and coloniality of knowledge. The study is focused on understanding the dynamics of the violent May 2008 attacks that took place in Alexandra and Yeoville. It problematised the use of the term xenophobia. The term occludes rather than enlightening the complex phenomenon of violence. Such violence has consistently and systematically engulfed people living in poor predominantly black areas of residence such as Yeoville and Alexandra. The study also used empirical evidence collected from the field to support its central arguments. What has been understood as xenophobia is in actual fact, part of the manifestation and outcome of abject living conditions of the poor. This study argues that what manifests itself as xenophobia is an additional element to various forms of violence taking place in locales such as Alexandra and Yeoville, places that decolonial theorists term ‘zones of non-being,’ where violent death is a constitutive part of human existence. / Development Studies / M. A. (Development Studies)