Oversampling and Coarse Quantization for Signals

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On the Linear Discrepancy of Convolution

Dr. Sinan Güntürk

Department Of Mathematics, New York University

Abstract:   Linear discrepancy is a combinatorial object that measures how well solutions of a linear equation can be rounded to neighboring integer vectors. We analyze a class of rounding algorithms based on error diffusion that yield good upper bounds for the linear discrepancy of smoothing type convolution operators. We also discuss various problems that arise as the space dimension is increased from one to two and higher.