Research report details noise-shaped coefficients in discrete polynomial Fourier extension

This research report delves into the intricacies of noise-shaped one-bit coefficients within normalized discrete polynomial Fourier extension. It explores error analysis for first-order Sigma-Delta quantization, establishing an O(N^-1) approximation rate on compact parameter sets for specific parabolic phases. The study also derives higher-order finite-record identities and demonstrates O(N^-r) decay for rth-order noise-shaped errors under certain conditions. The report further includes extensions to various complex scenarios, such as multidimensional parameter families and correlated state models. AI

RANK_REASON The item is a research report published on arXiv detailing mathematical and computational methods. [lever_c_demoted from research: ic=1 ai=0.4]

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