COURSE UNIT TITLE

: WAVELETS AND APPLICATIONS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5081 WAVELETS AND APPLICATIONS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR HALIL ORUÇ

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The aim of this course is to present essential idea behind wavelets theory together with applications such as signal and image analysis. It is designed for engineers, scientists, statisticians and mathematicians interested in the basic mathematical ideas underlying Fourier analysis, wavelets and their applications.

Learning Outcomes of the Course Unit

1   1. Will be able to use classical Fourier theory
2   2. Will be able to apply Haar wavelets
3   3. Will be able to apply multiresolution analysis
4   4. Will be able to use spline wavelets
5   5. Will be to be able to analyse a signal or an image using wavelets software.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Orthogonal projections
2 Fourier series convergence
3 Fourier transform
4 Haar wavelets
5 Decomposition and reconstruction algorithms
6 Multiresolution analysis
7 Linear-phase filtering
8 Daubechies wavelets
9 Problems and discussion
10 Cardinal spline spaces
11 Construction of spline approximation
12 Spline wavelets
13 Application to signal analysis
14 Application to image analysis

Recomended or Required Reading

Albert Boggess, Francis J. Narcowich, A First Course in Wavelets with Fourier Analysis-Wiley, 2009.
Referanslar:
Stephane Mallat, A Wavelet Tour of Signal Processing, Academic Press, Elsevier Inc. 3rd ed. 2009.
Charles Chui, An Introduction to Wavelets, Academic Press 1992.
George Bachman; Lawrence Narici; Edward Beckenstein , Fourier and Wavelet analysis, Springer 2002.
Lesley Ward, Harmonic Analysis: From Fourier to Wavelets , Student Mathematical Library Series, Volume 63, American Mathematical Society 2012.

Planned Learning Activities and Teaching Methods

Lecture notes,Presentation, Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

Mid Term Exam, Assignement+Presentation, Final Exam

Language of Instruction

English

Course Policies and Rules

%70 attendence mandatory.

Contact Details for the Lecturer(s)

Email: : halil.oruc@deu.edu.tr
Ofis: (232) 301 85 77, B205
DEÜ Fen Fakültesi Matematik Bölümü, Tınaztepe

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 12 4 48
Preparation for midterm exam 1 15 15
Preparation for final exam 1 30 30
Preparing assignments 1 35 35
Final 1 3 3
Midterm 1 3 3
TOTAL WORKLOAD (hours) 176

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.1453354353
LO.24443433
LO.34453453
LO.44453453
LO.55555453

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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