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Proceedings Paper

Analog to digital conversion for finite frames
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Paper Abstract

Sigma-Delta (ΣΔ) schemes are shown to be an effective approach for quantizing finite frame expansions. Basic error estimates show that first order ΣΔ schemes can achieve quantization error of order 1/N, where N is the frame size. Under certain technical assumptions, improved quantization error estimates of order (logN)/N1.25 are obtained. For the second order ΣΔ scheme with linear quantization rule, error estimates of order 1/N2 can be achieved in certain circumstances. Such estimates rely critically on being able to construct sufficiently small invariant sets for the scheme. New experimental results indicate a connection between the orbits of state variables in ΣΔ schemes and the structure of constant input invariant sets.

Paper Details

Date Published: 17 September 2005
PDF: 9 pages
Proc. SPIE 5914, Wavelets XI, 591416 (17 September 2005); doi: 10.1117/12.612909
Show Author Affiliations
John J. Benedetto, Univ. of Maryland (United States)
Alexander M. Powell, Princeton Univ. (United States)
Ozgur Yilmaz, The Univ. of British Columbia (Canada)

Published in SPIE Proceedings Vol. 5914:
Wavelets XI
Manos Papadakis; Andrew F. Laine; Michael A. Unser, Editor(s)

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