Wavelets: an overview, with recent applications

Summary form only given. Wavelets have emerged in the last decade as a synthesis from many disciplines, ranging from pure mathematics (where forerunners were used to study singular integral operators) to electrical engineering (quadrature mirror filters), borrowing in passing from quantum physics, from geophysics and from computer aided design. The author presents an overview of the ideas in wavelet theory, and shows how it fits into the different disciplines in which it is rooted. Some recent applications are discussed, including a nonlinear "squeezing" of the wavelet transform, inspired by auditory models, with applications to speech processing; and a discussion of the nonlinear approximation and why wavelets are so successful in the nonlinear approximation.