Global tile attractor of second order single-bit Sigma-Delta modulation.
Item
-
Title
-
Global tile attractor of second order single-bit Sigma-Delta modulation.
-
Identifier
-
AAI3310611
-
identifier
-
3310611
-
Creator
-
Zeng, Sidong.
-
Contributor
-
Adviser: Truong-Thao Nguyen
-
Date
-
2008
-
Language
-
English
-
Publisher
-
City University of New York.
-
Subject
-
Engineering, Electronics and Electrical
-
Abstract
-
As a widely used technology of modern A/D data conversion, high resolution Sigma-Delta (SigmaDelta) modulation keeps simple structure. However, its most fundamental mechanisms are difficult to analyze rigorously without modeling assumptions. This is due to the embedded nonlinear feedback. Following dynamical system approach, the goal of this thesis is to characterize the attractor of second order single-bit sigma-delta modulation. More precisely, we prove that the global attractor is a single tile. This work enables the rigorous analysis of the quantization error spectrum without any modeling assumption. The attractor is known as the finite union of disjointed tiles (up to a 0-measure set) so far under stability conditions.;In this thesis, a framework based on Lyapunov functions is established to prove that the system is globally stable. A family of Lyapunov functions are discovered. Trapping sets are generated systematically in a conceptual and direct way. The dynamical behavior inside a positively invariant set is also studied. As a theorem, if a positively invariant set can be split into two sets by the graph of a function and one of the subsets is positively invariant, such subset is automatically a trapping set. This technique applies to trapping sets generated under the framework based on Lyapunov functions. Smaller trapping sets are obtained such that none of them is possible to contain two disjointed tiles. This implies that the attractor is a tile.
-
Type
-
dissertation
-
Source
-
PQT Legacy CUNY.xlsx
-
degree
-
Ph.D.
