Course details
A specialist MAGIC course
Semester
- Spring 2021
- Monday, January 25th to Friday, March 19th; Monday, April 26th to Friday, May 7th
Hours
- Live lecture hours
- 10
- Recorded lecture hours
- 0
- Total advised study hours
- 40
Timetable
- Mondays
- 10:05 - 10:55 (UK)
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.
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.
Prerequisites
Some experience of Fourier series, Fourier transforms, and Hilbert spaces.
Syllabus
- Introduction and revision of Fourier series and transforms. (1)
- The Haar wavelet and the idea of a multiresolution expansion. (2)
- Paley-Wiener spaces, the sampling theorem, and Littlewood-Paley wavelets. (2)
- Riesz bases and frames. (2)
- Windowed Fourier transforms, Heisenberg's inequality, and wavelet transforms. (3)
Lecturer
-
JP
Professor Jonathan Partington
- University
- University of Leeds
Bibliography
Follow the link for a book to take you to the relevant Google Book Search page
You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.
Assessment
The assessment for this course will be released on Monday 10th May 2021 at 00:00 and is due in before Monday 24th May 2021 at 11:00.
Assessment will be by a take-home exam with a pass mark of 50%.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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