In this thesis, new effective and efficient implementation structures of three-dimensional (3D) spatio-temporal (ST) Finite Impulse Response (FIR) uniform and non-uniform cone and frustum filters using well-known filter banks are investigated. The performance of the proposed implementation structures for 3D ST FIR uniform and non-uniform cone and frustum filters are investigated for 3D broadband beamforming in radio astronomy applications. First, implementations of two 3D ST uniform FIR cone filters are investigated. The 3D cone filters are designed by cascading either the well-known uniform quadrature mirror – cosine-modulated (QM-CM) filter bank or directly designed filter banks (DDFBs), with 2D low-pass circularly-symmetric spatial filters. In addition, two 3D ST uniform FIR frustum filters are derived from the cone filters by implementing partial bands of the filter banks with corresponding 2D spatial filters. The performance of the proposed implementation structures for 3D ST uniform QM-CM and DDFBs cone and frustum filters are evaluated using broadband beamforming signals in radio astronomy applications. The performance of the QM-CM and DDFBs cone and frustum filters shows improvement in terms of Signal-to-Interference-plus-Noise ratio (SINRs) over existing 3D ST cone and frustum filters. In addition to their effective performance, these cone and frustum filters can be efficiently implemented with equivalent or less computational complexity compared to existing methods. Second, implementations of two 3D ST non-uniform cone and frustum filters are explored. These cone and frustum filters are obtained by cascading either QM-CM or DDFBs non-uniform filter banks, with 2D low-pass circularly-symmetric spatial filters. The motivation for the 3D ST non-uniform cone and frustum filters is to achieve better approximation at low temporal frequencies than using the uniform ones. The performance of the 3D ST non-uniform cone and frustum filters is evaluated and compared with the performance of the uniform 3D ST cone and frustum filters. Results indicate that the performance of the proposed 3D ST non-uniform QM-CM and DDFBs cone filters shows some improvement in selective filtering compared to the performance of 3D ST uniform cone filters. / Graduate / 0544 / hussamss@uvic.ca

In this thesis, multidimensional signal processing techniques to mitigate disturbances in synthetic aperture systems such as radio telescopes are investigated. Here, two computationally efficient three-dimensional (3D) spatio-temporal (ST) finite impulse response (FIR) cone filter bank structures are proposed. Furthermore, a strategy is proposed to design 3D ST FIR frustum filter banks, having double-frustum-shaped passbands oriented along the temporal axis, derived from appropriate 3D ST FIR cone filter banks. Both types of cone and frustum filter banks are almost alias free and provide near-perfect reconstruction. In the proposed cone and frustum filter banks, both temporal and spatial filtering operations can be carried out at a significantly lower rate compared to previously reported 3D ST FIR cone filter banks implying lower power consumption. Furthermore, the proposed cone and frustum filter banks require a significantly lower computational complexity than previously reported 3D ST FIR cone and frustum filter banks. Importantly, this is achieved without deteriorating the improvement in signal-to-interference-plus-noise ratio. A theoretical analysis of brightness distribution (BD) errors caused by parameter perturbations and mismatches among the transfer functions of receivers employed in synthetic aperture systems is presented. First, the BD errors caused by perturbations in the transfer functions of low noise amplifiers (LNAs) and anti-aliasing filters (AAFs) are considered, and the characteristics of the additive BD error and its effects on synthesized BDs are thoroughly analyzed. Second, the conditions that should be satisfied by the transfer functions of digital beamformers to eliminate the BD errors caused by their phase responses are examined. The sufficient condition to eliminate the BD errors is that the transfer functions are matched, and, interestingly, the phase responses are not necessary to be linear. Furthermore, the BD errors caused by typical tolerances of passive L and C elements used to implement the AAFs and those caused by the random variations of gain from LNA to LNA are quantified through numerical simulations. The simulations indicate that substantial BD errors are observed at frequencies that are close to the passband edge of the AAFs. / Graduate