The lower bound of the PCM quantization error in high dimensions

DOI10.1016/j.acha.2014.06.001zbMath1301.42056arXiv1403.4311OpenAlexW2962928403MaRDI QIDQ466980

Zhiqiang Xu, Heng Zhou

Publication date: 3 November 2014

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.4311

zbMATH Keywords

orthogonal polynomialsBessel functionsPCM quantization errorunit-norm tight frames

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Trigonometric polynomials, inequalities, extremal problems (42A05)

Related Items (2)

Improvement of the lower bound of the PCM quantization error for vectors in \(\mathbb{R}^2\) ⋮ Memoryless scalar quantization for random frames

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Lattice quantization error for redundant representations
• Second-order sigma-delta (\(\Sigma \Delta\)) quantization of finite frame expansions
• Pointwise comparison of PCM and \(\Sigma \Delta \) quantization
• The Performance of PCM Quantization Under Tight Frame Representations
• Sigma-delta (/spl Sigma//spl Delta/) quantization and finite frames
• Decision procedure for indefinite hypergeometric summation
• Quantized overcomplete expansions in IR/sup N/: analysis, synthesis, and algorithms
• Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigma-delta modulation
• White Noise Hypothesis for Uniform Quantization Errors

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