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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.


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


  • Mon 12:05 - 12:55


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


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)


Jonathan Partington
Phone (0113) 3435123
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Amos Ajibo
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Asmahan Alajyan
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Fadhel Almalki
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Afredo Garbuno Inigo
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Alexander Hindle
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Adam Horwich
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Andrzej KUCIK
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Jane Lyle
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Georgia Lynott
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Alexander Owen
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Rathish Ratnasingam
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Andrew Turner


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


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The course will be assessed by a take-home examination in April. There will be four questions, and you will need to obtain 50 percent to pass.

Examination for MAGIC094 Classical Wavelet Theory

Files:Exam paper
Released: Monday 24 April 2017 (333.6 days ago)
Deadline: Sunday 7 May 2017 (319.6 days ago)


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Recorded Lectures

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