COURSE UNIT TITLE

: WAVELET THEORY AND MULTIRESOLUTION SIGNAL ANALYSIS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
EEE 5067 WAVELET THEORY AND MULTIRESOLUTION SIGNAL ANALYSIS ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR GÜLAY TOHUMOĞLU

Offered to

ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)
ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)
ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)

Course Objective

Students are able to learn that what the wavelets are and the main differences between Fourier Transform and Wavelet transform. Students are able to know multi-resolution analysis and application on the different 1D and 2D signals.

Learning Outcomes of the Course Unit

1   The students are expected to learn what wavelets is, and the differences between Fourier Transform, Short Time Fourier Transform and Wavelet Transform and
2   The students are expected to understand the different wavelet types, analysis and synthesis by writing programmes
3   The students are expected to solve problems in wavelet domain by hand and/or writing programmes
4   The students are expected to gain basic skills about the application of WT for 1D and/or 2D signals as coding, noise elimination etc.
5   The students are expected to prepare a technical report related with the term project

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Review of Fourier transform, Short time Fourier Transform, Introduction to wavelets
2 Wavelets and wavelet expansion system
3 Wavelet Tutorial I, Amaras
4 Wavelet Tutorial I and II, Robi Polikar
5 Multiresolution Formulation of Wavelet Systems, Signal Spaces The Scaling function Multiresolution Analysis, The Wavelet Functions
6 Filter Bank and the Discrete Wavelet transform Anlysis-From Fine Scale to Coarse Scale, Filtering and Down-sampling or Decimating
7 Synthesis- From Coarse Scale to Fine Scale, Filtering and Up-sampling or Streching
8 Midterm Exam
9 Bases, orthogonal bases, Biorthogonal bases, Frames, Tight frames and Unconditional bases, The Scaling Function and Scaling coefficients, Wavelet and Wavelet Coefficients
10 Generalization of the Basic Multiresolution Wavelet System
11 Wavelet packets, multiwavelets
12 Discrete multiresolution analysis, the Discrete-time WT, CWT, Analogies of between Fourier Systems and Wavelet Systems
13 Discussion on the applications of wavelets on different areas, as coding, denoising of signals
14 Applications to 1D and 2D signals with MATLAB

Recomended or Required Reading

Burrus, C. Sidney Gopinath, R.A. and Guo, Haitao.
Introduction to Wavelets and Wavelet transforms, A Primer, Prentice Hall, 1998, ISBN: 0-13-489600-9

Supplementary Book(s):
1. Martin VETTERLI and Helena KOVACEVIC Wavelets and Subband Coding, Prentice Hall N. J. 1995 ISBN : 0-13-097080-8
2. Stéphane Mallat, A Wavelet Tour of Signal Processing, Second Edition (Wavelet Analysis & Its Applications), Academic Press, 1998,1999, ISBN : 0-12-466606-x

Materials:
Wavelet Tutorial I; Amaras
Wavelet Tutorial I, II, III, and IV; Robi Polikar

Planned Learning Activities and Teaching Methods

Lectures,
Compulsary to attend classroom
Each week Homework, These will be affected by the 20% rate,
1-Midterm Exam is 20%, Term Project is 20%, and Final Exam is 40%,

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.20 + ASG * 0.40 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.20 + ASG * 0.40 + RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

Compulsary to attend classroom
Each week Homework, These will be affected by the 20% rate,
1-Midterm Exam is 20%, Term Project is 20%, and Final Exam is 40%,

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

gulay.tohumoglu@deu.edu.tr

Office Hours

Friday From 10:30 to 11:30

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparation for midterm exam 1 8 8
Preparation for final exam 1 10 10
Preparing assignments 12 4 48
Design Project 1 40 40
Preparations before/after weekly lectures 13 3 39
Preparation for quiz etc. 10 1 10
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 200

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15
LO.153
LO.23
LO.3333
LO.443454
LO.55333444

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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