《Wavelet Analysis》Course Syllabus
Author:管理员 Time:2017-04-11 Hit:248

《Wavelet Analysis》Course Syllabus

Course Name

Wavelet Analysis

Instructor

Dr. Guoyong Qiu

Dr. Bing Xiao

Course Type

Selective Course

Prerequisite Courses

Calculus, Series,

Functional Analysis

Discipline

Computer Science

Learning Method

Mentoring,

Studying on one's own

Semester

1st semester

Hours

40

Credit

2

 

1. Objective & Requirement

Wavelets provide a powerful and remarkably flexible set of tools for handling fundamental problems in science and engineering. In recent times enormous interest has emerged in the application of wavelets, and they have been successfully implemented into many fields of endeavor ranging from data compression and signal processing through to the more mathematically pure field of solving partial differential equations. Wavelets provide an alternative approach to traditional signal processing techniques such as Fourier analysis for breaking a signal up into its constituent parts. The driving impetus behind wavelet analysis is their property of being localized in time (space) as well as scale (frequency). This provides a time-scale map of a signal, enabling the extraction of features that vary in time. This makes wavelets an ideal tool for analyzing signals of a transient or non-stationary nature.

This course provides a basic introduction to wavelets and their applications. The objective of this course is to establish fundamental concepts on wavelet analysis. The course will be taught in full English, and graduate students are welcome to attend the lectures. The prerequisite for the course are basics of calculus, series, and functional analysis.

 

2. Topics to be covered

We will cover the following core topics:

(I) Preliminaries: functional spaces( linear spaces, distance spaces, normed linear spaces, inner product spaces, Hilbert spaces), bases, orthonormal basis, Fourier analysis and transform

(II) Wavelet analysis: time-frequency analysis, continuous wavelet transforms, discrete wavelet transforms, popular wavelets

(III) MRA(Multiresolution analysis): MRA, scaling functions, wavelet functions, orthogonal scaling function, orthogonal wavelet functions, double scale equation

(IV) Mallat Algorithms: Mallat decomposition algorithm, Mallat reconstruction algorithm, orthogonal wavelet packet analysis

(V) Applications

3. Textbook

D. Lee Fugal, Conceptual Wavelets in Digital Signal Processing. SpaceTechnologies LLC, 2009.

4. Reference Books

 [1] Michel Misiti, etc., Wavelet Toolbox-For Use with MATLAB. The Mathworks, Inc., 1996.

 [2] Stephane Mallat, A wavelet tour of signal processing (Third Edition). State University of Elsevier Inc., 2009.

 [3] James S. Walker, A Primer on Wavelets and Their Scientific Applications (Second Edition). TaylorFrancis Group, LLC, 2008.

 [4] Ingrid Daubechies, Ten Lectures on Wavelets. SIAM, 1992.

5. Course Evaluation

  Article Reviewing                      50%

  Exam (in-class)                      50%