Ten lectures on wavelets
Introduction to Algorithms
Quantized overcomplete expansions in IRN: analysis, synthesis, and algorithms
IEEE Transactions on Information Theory
Noise reduction in oversampled filter banks using predictive quantization
IEEE Transactions on Information Theory
Multiple-description coding by dithered delta-sigma quantization
IEEE Transactions on Information Theory
Performance of sigma-delta quantizations in finite frames
IEEE Transactions on Information Theory
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Quantization noise shaping is commonly used in oversampled A/D and D/A converters with uniform sampling. This paper considers quantization noise shaping for arbitrary finite frame expansions based on generalizing the view of first-order classical oversampled noise shaping as a compensation of the quantization error through projections. Two levels of generalization are developed, one a special case of the other, and two different cost models are proposed to evaluate the quantizer structures. Within our framework, the synthesis frame vectors are assumed given, and the computational complexity is in the initial determination of frame vector ordering, carried out off-line as part of the quantizer design. We consider the extension of the results to infinite shift-invariant frames and consider in particular filtering and oversampled filter banks.