We define and study the generalized continuous wavelet transform associated with the Riemann-Liouville operator that we use to express the new inversion formulas of the Riemann-Liouville operator and its dual.

Various techniques have been developed to interpret potential field data which are broadly categorized as: Forward and Inverse modeling (Blakely, 1995). Ambiguity in identification and characterization of the sources from the potential field data makes formulation of initial model a critical step while analyzing the data. The second category of techniques (inversion) shows many constraints such...

This paper addresses the problem of multiplicative jump detection and estimation in the time-scale plane. The signature is derived for a multiplicative jump in the time-scale plane. The signature allows the study of two wavelet based detectors. The first detector computes the Continuous Wavelet Transform (CWT) correlation with 2D signature. The second detector sums k e d scale slices of the CWT...

In this paper we consider the conformal group of the unit sphere S, the proper Lorentz group Spin(1, n), for the study of spherical continuous wavelet transforms. The parameter space is determined by the factorization of the gyrogroup of the unit ball by an appropriate gyro-subgroup. We study two families of sections that give rise to anisotropic conformal dilation operators for the unit sphere...

Disk imbalance is a condition in which the center of mass of a rotating disk is not coincident with the center of rotation. Imbalance in a rotor system is unavoidable and it cannot be completely eliminated. Due to some reasons, such as porosity in casting, non-uniform density of material, manufacturing tolerances, and gain or loss of material during the operation, there is imbalance in rotors. ...

Electricity is considered a new commodity, mainly since the start of the electricity markets liberalization. However it represents an increasingly important sector of trading and as such a challenging area of research. Here we focus on the role of electricity power exchanges for the creation of a single European electricity market, on a di¤erent empirical perspective. We use daily power exchang...

Wavelet based time frequency representations of various signals are shown to reliably represent perceptually relevant patterns at various spatial and temporal scales in a noise robust way. Here we present a wavelet based visualization and analysis tool for prosodic patterns, in particular intonation. The suitability of the method is assessed by comparing its predictions for word prominences aga...

Wavelet Transformations and music have several things in common: both have something to do with time-frequency descriptions and constant relative bandwidth analysis. In this paper, we describe some applications of the Continuous Wavelet Transform in the processing of music. The main applications are analysis and pitch-shifting (or the equivalent time-stretching), for which we give an algorithm.

We introduce a framework for calculating sparse approximations to signals based on elements of continuous wavelet systems. The method is based on an extension of the continuous wavelet theory. In the new theory, the signal space is embedded in larger abstract signal space, which we call the window-signal space. There is a canonical extension of the wavelet transform on the window-signal space, ...

We propose an equivalence class of nonstationary Gaussian stochastic processes defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well-defined time-dependent spectral properties. They allow one to generate realizations of any wavelet spectrum. Based on this framework, we study the estimation of continuous wavelet spectra, i.e., we calcul...