Alternative dual frames for digital-to-analog conversion in sigma-delta quantization

DOI10.1007/s10444-008-9088-1zbMath1181.94050OpenAlexW2126749541MaRDI QIDQ849068

Alexander M. Powell, Özgür Yılmaz, Mark C. Lammers

Publication date: 24 February 2010

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-008-9088-1

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Approximations and expansions (41A99) Rate-distortion theory in information and communication theory (94A34)

Related Items

Sigma delta quantization with harmonic frames and partial Fourier ensembles, Quantization and Compressive Sensing, On description of dual frames, Sigma Delta Quantization for Images, Sobolev duals for random frames and \(\varSigma \varDelta \) quantization of compressed sensing measurements, Local sampling and approximation of operators with bandlimited Kohn-Nirenberg symbols, Quantization and Finite Frames, An uncertainty principle for finite frames, Sobolev duals in frame theory and Sigma-Delta quantization, Noise-Shaping Quantization Methods for Frame-Based and Compressive Sampling Systems, Distributed noise-shaping quantization. I: Beta duals of finite frames and near-optimal quantization of random measurements, A note on finite dual frame pairs, Dynamical dual frames with an application to quantization

Cites Work

• Unnamed Item
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• Second-order sigma-delta (\(\Sigma \Delta\)) quantization of finite frame expansions
• Frame paths and error bounds for sigma-delta quantization
• Characterization of oblique dual frame pairs
• Sobolev duals in frame theory and Sigma-Delta quantization
• Approximating a bandlimited function using very coarsely quantized data: a family of stable sigma-delta modulators of arbitrary order
• The art of frame theory
• Stability analysis for several second-order Sigma-Delta methods of coarse quantization of bandlimited functions
• Finite normalized tight frames
• Pseudoframes for subspaces with applications
• Smooth frame-path termination for higher order sigma-delta quantization
• Sigma-delta (/spl Sigma//spl Delta/) quantization and finite frames
• The Validity of the Additive Noise Model for Uniform Scalar Quantizers
• Multiloop sigma-delta quantization
• A necessary and sufficient condition for quantization errors to be uniform and white
• Quantized overcomplete expansions in IR/sup N/: analysis, synthesis, and algorithms
• One-bit sigma-delta quantization with exponential accuracy
• Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigma-delta modulation
• Noise reduction in oversampled filter banks using predictive quantization
• On the whiteness of high-resolution quantization errors
• Resilience properties of redundant expansions under additive noise and quantization
• Portraits of Frames
• On general frame decompositions
• White Noise Hypothesis for Uniform Quantization Errors
• Quantized frame expansions with erasures