Smooth Frame-Path Termination for Higher Order Sigma-Delta Quantization |
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Authors: | Bernhard G Bodmann Vern I Paulsen Soha A Abdulbaki |
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Institution: | (1) Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;(2) Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204-3008, USA |
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Abstract: | We study the performance of finite frames for the encoding of vectors by applying standard higher-order sigma-delta quantization
to the frame coefficients. Our results are valid for any quantizer with accuracy ε > 0 operating in the no-overload regime.
The frames under consideration are obtained from regular sampling of a path in a Hilbert space. In order to achieve error
bounds that are comparable to results on higher-order sigma-delta for the quantization of oversampled bandlimited functions,
we construct frame paths that terminate smoothly in the zero vector, that is, with an appropriate number of vanishing derivatives
at the endpoint. |
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Keywords: | |
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