Abstract—A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be associated with a proper probability density, allowing defining the entropy of a wavelet. Introducing now the concept of wavelet mutual information between a signal and an analysing wavelet fulfils the foundati...

his report reviews the history, theory and mathematics of wavelet analysis. Examination of the Fourier Transform and Short-time Fourier Transform methods provides information about the evolution of the wavelet analysis technique. This overview is intended to provide readers with a basic understanding of wavelet analysis, define common wavelet terminology and describe wavelet analysis algorithms...

A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the local commutant of a system. This is really an abstract application of the theory of operator algebras to wavelet theory. The concrete applications of this m...

The recently developed theory of wavelets has a remarkable property to \zoom in" on very short lived frequency phenomena, such as transients in signals and singularities in functions, and hence provides an ideal tool to study localized changes. This paper proposes a wavelet method to estimate jump and sharp cusp curves of a function in the plane. The method is rst to compute wavelet transformat...

The theory of periodic wavelet transforms presented here was originally developed to deal with the problem of epileptic seizure prediction. A central theorem in the theory is the characterization of wavelets having time and scale periodic wavelet transforms. In fact, we prove that such wavelets are precisely generalized Haar wavelets plus a logarithmic term. It became apparent that the aforemen...

A brief survey of a paper by Peter Steffen, et al. Introduction G.K. Chesterton, an English author and journalist from the turn of the century, once stated he desired to write a story about a man setting sail from England in search of a new and foreign land. Eventually, when the man reached the island of his destination, he found it to be the most extraordinary and fascinating place. Unbeknowns...

We review the main methods combining wavelet to soft computing. The integration of wavelet theory into soft computing started more than ten years ago, using wavelet analysis essentially as a preprocessing method. The first real integration of wavelet into soft computing coincided to the development of wavelet-networks. In the last three years, an increasing number of applications of wavelet-net...

In this paper we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case we have the solution as a multiresolution expansion in the base of compactly supported wavelet basis. The solution is parametrized by the solutions of two reduced algebraical problems, one is nonlinear and the second is some li...