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Description

Developed mostly in the 1980s, wavelets provide an alternative to Fourier series with better localization properties, and have found applications in approximation, signal and image processing, areas of applied mathematics such as acoustics and electromagnetism, and also in statistics. This course gives a non-technical introduction to wavelets, focusing on the simplest examples, such as the Haar wavelets (which go back to 1909) and the Littlewood-Paley wavelets (based on ideas from the 1930s). It will also discuss windowed Fourier transforms and wavelet transforms, as ways of capturing local behaviour of functions/data.

Semester

Spring 2017 (Monday, January 23 to Friday, March 31)

Timetable

  • Mon 12:05 - 12:55

Prerequisites

Some experience of Fourier series, Fourier transforms, and Hilbert spaces.

Syllabus

1. Introduction and revision of Fourier series and transforms. (1) 2. The Haar wavelet and the idea of a multiresolution expansion. (2) 3. Paley-Wiener spaces, the sampling theorem, and Littlewood-Paley wavelets. (2) 4. Riesz bases and frames. (2) 5. Windowed Fourier transforms, Heisenberg's inequality, and wavelet transforms. (3)

Lecturer


Jonathan Partington
Email j.r.partington@leeds.ac.uk
Phone (0113) 3435123
vcard
Photo of Jonathan Partington


Students


Photo of Amos Ajibo
Amos Ajibo
(Newcastle)
Photo of Asmahan Alajyan
Asmahan Alajyan
(Leeds)
Photo of Fadhel Almalki
Fadhel Almalki
(Leeds)
Photo of Afredo Garbuno Inigo
Afredo Garbuno Inigo
(Liverpool)
Photo of Massimo Gisonni
Massimo Gisonni
(Loughborough)
Photo of Alexander Hindle
Alexander Hindle
(Newcastle)
Photo of Adam Horwich
Adam Horwich
(Birmingham)
Photo of Andrzej KUCIK
Andrzej KUCIK
(Leeds)
Photo of Jane Lyle
Jane Lyle
(Surrey)
Photo of Marianthi Moschou
Marianthi Moschou
(Manchester)
Photo of Alexander Owen
Alexander Owen
(Exeter)
Photo of Rathish Ratnasingam
Rathish Ratnasingam
(Newcastle)
Photo of Andrew Turner
Andrew Turner
(Birmingham)


Bibliography


Ten Lectures on WaveletsDaubechies
An Introduction to WaveletsChui
A Friendly Guide to WaveletsKaiser


Note:

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Assessment



The course will be assessed by a take-home examination. More details later.

No assignments have been set for this course.

Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1-10MAGIC094course.pdf
1-10MAGIC094ex1.pdf
1-10MAGIC094overheads.pdfL


Recorded Lectures


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