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WAVELETS
WITH APPLICATIONS FOR SCIENTISTS AND ENGINEERS Summer
Semester, 2000 SECTION
6111/6112:MTR 5:307:20 H 100 |
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INSTRUCTOR:Dr.
Weldon Wilson
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OFFICE:Howell
Hall 221H
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OFFICE
HOURS:MTR
4:305:20,or by arrangement
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PHONE:
(405) 974-5470
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EMAIL:wwilson@ucok.edu
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FAX:
(405) 974-3824
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COURSE
SYNOPSIS
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Wavelet
theory involves representing general functions in terms of simpler, fixed
functions at different scales and position. In the 1980's it was realized
that several different fields in Fourier and harmonic analysis, quantum
physics, signal processing and filtering were closely related.The
term wavelet theory represents a unified view of these different approaches,
and encompasses a general theoretical framework with applications to many
fields in mathematics, physics and engineering.Wavelets
have significant advantages over other methods for use in signal and image
compression (e.g digital television) and data storage (e.g. FBI fingerprint
database). This course covers the background material, which leads to the
theory of wavelets, multi-resolution analysis and filters. Computer packages
for wavelets will be used to illustrate the concepts. Applications of wavelets
to signal compression and filtering, image analysis and compression, modeling,
denoising, and restoration, and the solution of differential equations
will be addressed. An extensive introduction to MATLAB and its use is included
and one of the course goals is to develop a proficiency in the use of MATLAB.
No prior experience with MATLAB is assumed.
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PREREQUISITES
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A
basic knowledge of matrices and differential equations assumed. This class
is intended to be an elementary introduction to wavelets and should be
accessible to graduate students and advanced undergraduates in Statistics,
Mathematics, Computer Science, Physics and Engineering.
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TEXTBOOK
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Introduction
to Wavelets and Wavelet Transforms
A Primer,
by C. Sidney Burrus, Ramesh A. Gopinath and Haitao Guo, 1998, Prentice
Hall.
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HOMEWORK
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Homework
will be regularly assigned, collected and graded. Homework solutions should
be neatly written on standard notebook-size (8.5 x 11) paper using one
side only.It is helpful if the pages
are stapled together.For full
credit, homework solutions should clearly state the principles of physics
and/or formula used and fully explain all reasoning.
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EXAMS
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There
will be two in-class exams and a comprehensive final on the following dates:
Mid-Term
Thursday, July 6 @ 5:30-7:20
Final
Exam Monday, July 31 @ 5:30-7:30 Students
who miss an exam should contact their instructor as soon as possible to
schedule a makeup.Exams will
consist of questions and problems similar to those assigned for homework. |
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GRADES
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Grades
will be class curved with a target class GPA of ~2.8 but in no event will
the curve be stricter than the straight curve listed below or lower than
the lowest curve shown below.Graduate
students will be graded on a separate scale from undergraduates. Undergraduates
will have different tests and homework assignments.
Typical
Class Curves Range
PointsStraight
CurveLowest CurveTypical
Grade Distribution Midterm
Exam100 (25%)A
(Above 90%)A (Above 85%)A
(~25% of Class) Homework100
(25%)B (81% 90%)B
(66% 85%)B (~40% of Class) Project/Report100
(25%)C (71% 80%)C
(51% 65%)C (~35% of Class) Final
Exam100 (25%)D
(60% 70%)D (40% 50%)D/F
(~0% of Class) Total400
(100 %)F (Below 60%)F
(Below 40%) |
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SPECIAL
ACCOMODATIONS
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Students
with disabilities who believe that they may need accommodations in this
class are encouraged to contact Equity Officer Brad Morelli at ext. 2573,
or see me after class as soon as possible to ensure that such accommodations
are implemented in a timely fashion.
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PHY
4913/5553
WAVELETS LECTURES
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WEEK |
DATE |
LECTURETOPIC |
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M JUN 5
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Introduction / Introduction
to MATLAB Tutorial
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T JUN 6
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Introduction to MATLAB
Tutorial (Continued)
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R JAN 8
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Introduction to MATLAB
Tutorial (Continued)
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M JUN 12
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AdvancedMATLAB
Programming
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T JUN 13
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Advanced MATLAB Tutorial
Programming (Continued)
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R JUN 18
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Advanced MATLAB Tutorial
Programming (Continued)
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M JUN 19
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Fourier Series and Transforms
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T JUN20
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Spectral Analysis and
the Fast Fourier Transform
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R JUN 22
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Solving ODEs with Fourier
Transform
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M JUN 26
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Applications ofFourier
Transforms
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T JUN 27
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Introduction to Wavelets
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R JUN 29
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Scaling and Wavelets
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M JULY 3
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NO CLASS INDEPENDENCE
DAY HOLIDAY!!!
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T JULY 4
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NO CLASS INDEPENDENCE
DAY HOLIDAY!!!
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R JULY 6
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MIDTERM EXAM
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M JULY 10
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Haar Wavelets
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T JULY 11
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Introduction to Multi-resolution
Analysis
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R JULY 13
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Daubechies Wavelets
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M JULY 17
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Fast Wavelet Transform
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T JAN 18
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Wavelets and Signal Analysis/Compression
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R JAN 20
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Wavelets and Image Processing
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M JULY 24
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Wavelets and Quantum
Mechanics
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T JULY 25
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Wavelet Electromagnetics
with Applications to Radar & Scattering
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R JULY 27
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Project Presentations*
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#9 |
M July 31
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5:30 - 7:30FINAL
EXAM!!
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*A
written project report is due on the last day of class and a 15-minute
oral presentation will be given to the class on the project. The project
should involve wavelets in some area of application of the students choosing
and involve a MATLAB program computation. A list of possible projects will
be provided during the third week of class along with other details and
requirements for the project.