Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigma-delta modulation

DOI10.1090/S0894-0347-03-00436-3zbMath1032.94502MaRDI QIDQ4441816

C. Sinan Güntürk

Publication date: 7 January 2004

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

samplingexponential sumsdiscrepancyuniform distributionmodulationsignal representationsigma-delta quantization

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Rate of convergence, degree of approximation (41A25) General theory of distribution modulo (1) (11K06) Modulation and demodulation in information and communication theory (94A14)

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Second-order sigma-delta (\(\Sigma \Delta\)) quantization of finite frame expansions, Alternative dual frames for digital-to-analog conversion in sigma-delta quantization, ON COARSE QUANTIZATION OF TIGHT GABOR FRAME EXPANSIONS, Frame paths and error bounds for sigma-delta quantization, Sigma-Delta Quantization for Fusion Frames and Distributed Sensor Networks, Pointwise comparison of PCM and \(\Sigma \Delta \) quantization, The lower bound of the PCM quantization error in high dimensions, An optimal family of exponentially accurate one-bit Sigma-Delta quantization schemes, Randomly dithered quantization and sigma-delta noise shaping for finite frames, Mathematics of Analog‐to‐Digital Conversion, Quantization and Finite Frames, Sigma-delta quantization errors and the traveling salesman problem, Sobolev duals in frame theory and Sigma-Delta quantization, Ergodic dynamics in sigma-delta quantization: tiling invariant sets and spectral analysis of error, High-order low-bit Sigma-Delta quantization for fusion frames, Quantization for spectral super-resolution

Cites Work

• Approximating a bandlimited function using very coarsely quantized data: a family of stable sigma-delta modulators of arbitrary order
• Refined Error Analysis in Second-Order<tex>$Sigma Delta $</tex>Modulation With Constant Inputs
• One-bit sigma-delta quantization with exponential accuracy
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