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)/N^1.25 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.

Date Published: 17 September 2005
PDF: 9 pages
Proc. SPIE 5914, Wavelets XI, 591416 (17 September 2005); doi: 10.1117/12.612909

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