English(EN) Research Report on Noise-Shaped One-Bit Coefficients in Discrete Polynomial Fourier Extension

研究报告详述离散多项式傅里叶扩展中的噪声整形单比特系数

作者 PulseAugur 编辑部 · [1 个来源] · 2026-07-26 21:51

本研究报告深入探讨了归一化离散多项式傅里叶扩展中的噪声整形单比特系数，重点关注一阶Sigma-Delta量化。该研究为抛物线相位函数建立了O(N^-1)的逼近率，并证明了该速率对于可容许输入类别是尖锐的。研究结果扩展到更高阶的有限记录恒等式，在特定条件下，为光滑权重提供了O(N^-r)衰减，为C^(r-1,α)权重提供了O(N^-(r-1+α))衰减。报告还详细介绍了精确的L2正交恒等式、四阶矩公式、局部核估计和振荡传递界，并将其扩展到更复杂的参数族和模型。 AI

影响该研究为信号处理技术提供了理论基础，这些技术可能应用于AI模型压缩和高效数据表示。

排序理由该项目是一份研究报告，详细介绍了数学方法和理论发现。[lever_c_demoted from research: ic=1 ai=0.7]

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Hugging Face Daily Papers TIER_1 English(EN) · 2026-07-26 21:51

离散多项式傅里叶扩展中噪声整形单比特系数的研究报告

This report studies noise-shaped one-bit coefficients in normalized discrete polynomial Fourier extension. For first-order Sigma-Delta quantization, the error is written as $e_k=u_k-q_k=Δv_k$ with a uniformly bounded state. Discrete summation by parts then yields variation estima…

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离散多项式傅里叶扩展中噪声整形单比特系数的研究报告

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