Introduces the basics of Fourier analysis as a prelude to applications. The course develops Fourier analysis from a general pure mathematical perspective starting with Lebesgue integration and elements of the theory of Hilbert spaces, leading to Fourier series, Fourier integrals and the fast Fourier transform, and then to applications such as partial differential equations and sampling. These subjects are of great importance to the electrical engineering and physics communities. The course concludes with more modern topics such as Gabor and wavelet transforms.
- Semester 1 - 2016
1. In-depth knowledge of Fourier analysis and its applications to problems in physics and electrical engineering.
2. An ability to communicate reasoned arguments of a mathematical nature in both written and oral form.
3. An ability to read and construct rigorous mathematical arguments.
- Basics of Lebesgue integration
- Elements of Hilbert spaces and orthogonal expansions
- Fourier series and Fourier transforms of continuous data; applications to partial differential equations, sampling and uncertainty
- Fast Fourier transform of discrete data
- Time-frequency and time-scale analysis
MATH2320 and MATH2330
In Term Test: Class Test
Written Assignment: Homework assignments (x5)
Presentation: Presentation (x5)
Formal Examination: Examination ¿ Formal
Face to Face On Campus 3 hour(s) per Week for Full Term