Conference Main
Course 6

From Fourier Analysis to Wavelets

Fourier analysis and wavelet theory, the fundamental mathematical framework for the description of functions in the time and frequency domains, are the key elements for effective analysis of function properties, as well as for efficient implementation of computational methods. For this reason, it is very important in many application areas to find function descriptions that are localized both in time and frequency. In this course, attendees learned the mathematical concepts behind Fourier analysis and wavelets. These concepts are significant for researchers and developers alike, because they are involved in so many of the problems in computer graphics and image processing.

Knowledge of linear algebra and calculus. Some familiarity with analysis of real and complex functions desirable. The course also assumed basic knowledge of signal and image processing.

Topics Covered
The main tools for function analysis in the frequency domain (the Fourier and Windowed Fourier Transforms), fundamental aspects of multiresolution analysis and its importance to the construction of wavelets, the main principles of computation with wavelets and their implementation, and various extensions of the basic wavelet transform.

Organizers and Lecturers
Jonas Gomes
Luiz Velho
Instituto de Matemática Pura e Aplicada

Main Comments and questions