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Discretization and reconstruction are fundamental operations in computer graphics, enabling the conversion between sampled and continuous representations. Major advances in signal processing research have shown that such operations can often be performed more efficiently by decomposing a filter into two parts: a compactly-supported continuous-domain function and a digital filter. This strategy of "generalized sampling" has appeared in a few graphics papers, but is largely unexplored within the computer graphics community. A Fresh Look at Generalized Sampling broadly summarizes the key aspects of generalized sampling, and delves into specific applications in graphics. Using new notation, it concisely presents and extends several key techniques. In addition, it demonstrates benefits for prefiltering in image downscaling and supersample-based rendering, and presents an analysis of the associated variance reduction. It concludes with a qualitative and quantitative comparison of traditiona and generalized filters. A Fresh Look at Generalized Sampling is an ideal primer for graphics researchers interested in generalized sampling methods and how they might apply them.