Course syllabus - Wavelets

Objectives

The objective of the course is to present many essential ideas behind wavelet analysis along with some of their applications to signal analysis to an audience of advanced graduate and PhD students with mathematical and engineering background.
 

Learning outcomes

At the end of the course the student is expected to be able to:

- Use the windowed Fourier transform to give information about signals simultaneously in the time domain and frequency domain.
- Use the continuous wavelet transforms to analyze the signal’s regular time behavior that is either very rapid or very slow.
- Analyze and reconstruct signals, using the theory of generalized frames.
- Recover signals using a discrete subset of notes.
- Perform discrete time-scale analysis and reconstruct signals as a discrete superposition of reciprocal wavelets.
- Perform discrete wavelet analysis and synthesis using recursive multi-resolution analysis with the help of orthonormal wavelets with prescribed locality and smoothness.

Course content

- Windowed Fourier transform
- Continuous wavelet transforms
- Generalized frames
- Discrete time-frequency analysis and sampling
- Discrete time-scale analysis
- Multiresolution analysis
- Daubechie’s orthonormal wavelet bases
- Applications to electromagnetics, scattering, and acoustics.

Tuition

Lectures and seminars.
 

Specific requirements

120 ECTS credits from one/some of the following areas: mathematics, computer science, engineering including Applied Mathematics7.5 ECTS credits or Applied Matrix Analysis, 7.5 ECTS credits or equivalent knowledge. In addition Swedish course B/Swedish course 3 and English course A/English course 6 are required. For courses given entirely in English exemption is made from the requirement in Swedish course B/Swedish course 3.

Examination

Examination (TEN1), 4,5 hp, credits 3, 4 eller 5
Seminar (SEM1), 3 hp, credits G
To obtain 4 or 5 on the course a 4 or 5 is required on TEN1

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass with credit, Pass, Fail