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