Orthonormal Wavelets

Abstract

The aim of this survey on the theory of wavelets is to help the scientific community to use wavelets as an alternative to the standard Fourier analysis. This survey is a written and extended version of a lecture I have been asked to give at the international conference held at Marseille on ondelettes, méthodestemps-fréquences et espaces des phases (December 14–18, 1987). This conference was a remarkable success. People with distinct scientific educations could communicate and interact, using the new born concept of wavelets. As often the flexibility of the concept helped a lot and during the lunches and dinners, physicians, physicists and even mathematicians were surprised and delighted to understand each other. Now my task is less pleasant and I have to do my job, giving precise definitions and describing specific algorithms. The advantage will be to prepare the ground for programming these algorithms.