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- Title
Alternative dual frames for digital-to-analog conversion in sigma–delta quantization.
- Authors
Lammers, Mark; Powell, Alexander; Yılmaz, Özgür
- Abstract
We design alternative dual frames for linearly reconstructing signals from sigma–delta (ΣΔ) quantized finite frame coefficients. In the setting of sampling expansions for bandlimited functions, it is known that a stable rth order sigma–delta quantizer produces approximations where the approximation error is at most of order 1 / λ r, and λ > 1 is the oversampling ratio. We show that the counterpart of this result is not true for several families of redundant finite frames for $\mathbb{R}^d$ when the canonical dual frame is used in linear reconstruction. As a remedy, we construct alternative dual frame sequences which enable an rth order sigma–delta quantizer to achieve approximation error of order 1/ N r for certain sequences of frames where N is the frame size. We also present several numerical examples regarding the constructions.
- Subjects
DIGITAL-to-analog conversion; CHEMICAL decomposition; NUMERICAL analysis; ELECTRONIC data processing; FRAMES (Combinatorial analysis)
- Publication
Advances in Computational Mathematics, 2010, Vol 32, Issue 1, p73
- ISSN
1019-7168
- Publication type
Article
- DOI
10.1007/s10444-008-9088-1