Where do wavelets come from? A personal point of view

The development of wavelets is an example where ideas from many different fields combined to merge into a whole that is more than the sum of its parts. The subject area of wavelets, developed mostly over the last 15 years, is connected to older ideas in many other fields, including pure and applied mathematics, physics, computer science, and engineering. The history of wavelets can therefore be represented as a tree with roots reaching deeply and in many directions. In this picture, the trunk would correspond to the rapid development of “wavelet tools” in the second half of the 1980´s, with shared efforts by researchers from many different fields; the crown of the tree, with its many branches, would correspond to different directions and applications in which wavelets are now becoming a standard part of the mathematical tool kit, alongside other more established techniques. The author gives here a highly personal version of the development of wavelets