Wavelets on Euclidean Spaces
Sabrine Arfaoui, Anouar Ben Mabrouk, Carlo Cattani · 2021
Wavelets were discovered in the eighteenth century in petroleum exploration, and since their discovery, they have proven to be powerful tools in many fields from pure mathematics to physics to applied ones such as images, signals, medicine, finance and statistics. This chapter proposes to review the basic concepts of wavelets as well as their basic properties. A wavelet transform is a representation of the signal by means of an integral form similar to Fourier one in which the Fourier sine and/or cosine is replaced by the analyzing wavelet. Wavelet bases are related to the concept of multiresolution analysis where an important property is also required and looks like the localization and consists of the existence of Riesz basis to define a multiresolution analysis.