Signals with sparse but otherwise unknown frequency content are well-represented by multi-coset samples, and efficient algorithms can be used to recover the underlying sparsity structure. While such sampling is usually analyzed over a sampling interval sufficiently large that edge effects can be ignored, in this work we develop how to take into account finite-window effects in system design. Such considerations are particularly important in the context of antenna arrays, and we analyze the associated redundancy. Additionally, we describe an efficient MIMO radar implementation of multi-coset arrays. As an example application of our results, we develop a natural two-stage architecture for direction-of-arrival estimation in sparse environments using a multi-coset array over the available aperture.