Abstract
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.
Highlights
Quantization methods for frame expansions have received considerable attention in the last few years
The method is algorithmically similar to classical first-order noise shaping and uses a quantity called frame variation to determine the optimal ordering of frame vectors such that the quantization error is reduced
In this paper we view noise shaping as compensation of the error resulting from quantizing each frame expansion coefficient through a projection onto the space defined by another synthesis frame vector
Summary
Quantization methods for frame expansions have received considerable attention in the last few years. The method is algorithmically similar to classical first-order noise shaping and uses a quantity called frame variation to determine the optimal ordering of frame vectors such that the quantization error is reduced. That solution performs higher-order noise shaping, where the error is filtered and subtracted from the subsequent frame coefficients. In this paper we view noise shaping as compensation of the error resulting from quantizing each frame expansion coefficient through a projection onto the space defined by another synthesis frame vector. This requires only knowledge of the synthesis frame set and a prespecified ordering and pairing for the frame vectors. We consider the case of reconstruction filterbanks, and how our work relates to [7]
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