Spectral CT is an emerging modality that uses a data acquisition scheme with varied spectral responses to provide enhanced material discrimination in addition to the structural information of conventional CT. Existing clinical and preclinical designs with this capability include kV-switching, split-filtration, and dual-layer detector systems to provide two spectral channels of projection data. In this work, we examine an alternate design based on a spatial-spectral filter. This source-side filter is made up a linear array of materials that divide the incident x-ray beam into spectrally varied beamlets. This design allows for any number of spectral channels; however, each individual channel is sparse in the projection domain. Model-based iterative reconstruction methods can accommodate such sparse spatial-spectral sampling patterns and allow for the incorporation of advanced regularization. With the goal of an optimized physical design, we characterize the effects of design parameters including filter tile order and filter tile width and their impact on material decomposition performance. We present results of numerical simulations that characterize the impact of each design parameter using a realistic CT geometry and noise model to demonstrate feasibility. Results for filter tile order show little change indicating that filter order is a low-priority design consideration. We observe improved performance for narrower filter widths; however, the performance drop-off is relatively flat indicating that wider filter widths are also feasible designs.