This thesis deals with design algorithms for filter banks based on optimization. The design specifications consist of the perfect reconstruction and frequency response specifications for finite impulse response (FIR) analysis and synthesis filters. The perfect reconstruction conditions are formulated as a set of linear equations with respect to the analysis filters’ coefficients and the synthesis filters’ coefficients. Five design algorithms are presented. The first three are based on an unconstrained optimization of performance indices, which include the perfect reconstruction error and the error in the frequency specifications. The last two algorithms are formulated as constrained optimization problems with the perfect reconstruction error as the performance index and the frequency specifications as constraints. The performance of the five algorithms is evaluated and compared using six examples; these examples include uniform filter bank, compatible non-uniform filter bank and incompatible non-uniform filter bank designs. The evaluation criteria are based on distortion and aliasing errors, the magnitude response characteristics of analysis and synthesis filters, the computation time required for the optimization, and the convergence of the performance index with respect to the number of iterations. The results show that the five algorithms can achieve almost perfect reconstruction and can meet the frequency response specifications at an acceptable level. In the case of incompatible non-uniform filter banks, the algorithms have challenges to achieve almost perfect reconstruction. / Graduate

A new broadband beamformer composed of nested arrays (NAs), multi-dimensional (MD) filters, and multirate techniques is proposed for both linear and planar arrays. It is shown that this combination results in frequency-invariant response. For a given number of sensors, the advantage of using NAs is that the effective aperture for low temporal frequencies is larger than in the case of using uniform arrays. This leads to high spatial selectivity for low frequencies. For a given aperture size, the proposed beamformer can be implemented with significantly fewer sensors and less computation than uniform arrays with a slight deterioration in performance. Taking advantage of the Noble identity and polyphase structures, the proposed method can be efficiently implemented. Simulation results demonstrate the good performance of the proposed beamformer in terms of frequency-invariant response and computational requirements. The broadband beamformer requires a filter bank with a non-compatible set of sampling rates which is challenging to be designed. To address this issue, a filter bank design approach is presented. The approach is based on formulating the design problem as an optimization problem with a performance index which consists of a term depending on perfect reconstruction (PR) and a term depending on the magnitude specifications of the analysis filters. The design objectives are to achieve almost perfect reconstruction (PR) and have the analysis filters satisfying some prescribed frequency specifications. Several design examples are considered to show the satisfactory performance of the proposed method. A new blind multi-stage space-time equalizer (STE) is proposed which can separate narrowband sources from a mixed signal. Neither the direction of arrival (DOA) nor a training sequence is assumed to be available for the receiver. The beamformer and equalizer are jointly updated to combat both co-channel interference (CCI) and inter-symbol interference (ISI) effectively. Using subarray beamformers, the DOA, possibly time-varying, of the captured signal is estimated and tracked. The estimated DOA is used by the beamformer to provide strong CCI cancellation. In order to alleviate inter-stage error propagation significantly, a mean-square-error sorting algorithm is used which assigns detected sources to different stages according to the reconstruction error at different stages. Further, to speed up the convergence, a simple-yet-efficient DOA estimation algorithm is proposed which can provide good initial DOAs for the multi-stage STE. Simulation results illustrate the good performance of the proposed STE and show that it can effectively deal with changing DOAs and time variant channels. / Graduate / 0544 / imanmoaz@uvic.ca