Second-order Sigma-Delta (ΣΔ) quantization of finite frame expansions

被引：43

作者：

Benedetto, JJ ^{[1
]}

Powell, AM

Yilmaz, Ö

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

[3] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2006年 / 20卷 / 01期

关键词：

quantization; second-order Sigma-Delta schemes; finite frames; stability;

D O I：

10.1016/j.acha.2005.04.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The second-order Sigma-Delta (Sigma Delta) scheme with linear quantization rule is analyzed for quantizing finite unit-norm tight frame expansions for R-d. Approximation error estimates are derived, and it is shown that for certain choices of frames the quantization error is of order 1/N-2, where N is the frame size. However, in contrast to the setting of bandlimited functions there are many situations where the second-order scheme only gives approximation error of order 1/N. For example, this is the case when quantizing harmonic frames of odd length in even dimensions. An important component of the error analysis involves extending existing stability results to yield smaller invariant sets for the linear second-order Sigma Delta scheme. (C) 2005 Elsevier Inc. All rights reserved.

引用

页码：126 / 148

页数：23

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