F005. Hubbard, B. B. [1998] The world according to wavelets the story of a mathematical technique in the making. 2 Edition, A K Peters. Qian, S. [2002] Introduction to time-frequency and wavelet transforms.

The continuous wavelet transform utilizing a complex Morlet analyzing wavelet has a close connection to the Fourier transform and is a powerful analysis tool for decomposing broadband wavefield data. A wide range of seismic wavelet applications have been reported over the last three decades, and the free Seismic Unix processing system now contains a code (succwt) based on the work reported here.

In this article, we introduce a kind of unitary operator U associated with the involution on the Heisenberg group, invariant closed subspaces are identified with the characterization spaces of sub-Laplacian operators. In the sense of vector-valued functions, we study the theory of continuous wavelet transform. Also, we obtain a new inversion formula of Radon transform on the Heisenberg group Hn.

The present study provides a concise description of wave propagation in cellular sandwich panels. A novel approach of damage detection based on mode conversion is proposed which can be useful for detecting relatively small damages in cellular sandwich structures using high frequency guided waves. The new methodology applies the continuous wavelet transform (CWT) and the cosine formula to extrac...

In this paper, a three Degrees of Freedom (DOF) model of a quarter vehicle suspension system is proposed including the seat driver mass. The modal parameters of this system, which indicate the comfort and the safety of the suspension, are identified using Wavelet analysis. Two applications of wavelet analysis are presented: signal denoising based on the Discrete Wavelet Transform (DWT) and moda...

Two methods to deconvolve experimental data from the distortions introduced by instrumental devices or source effects are presented. Considering a total acquistion system (emissionreception line, amplifier, pre-amplifier) as a global experimental filter, we can define its properties (module and phase) experimentally from the generation of a family of source signals dilated in time. The estimati...

Abstract: In this paper we consider time scale synchronization between two different timedelay systems. Due to existence of intrinsic multiple characteristic time scales in the chaotic time series, the usual definition for the calculation of phase failed. To define the phase, we have used empirical mode decomposition and the results are compared with those from continuous wavelet transform. We ...

We introduce a fast simple method for computing the real continuous wavelet transform (CWT). The approach achieves O N ( ) complexity per scale and the filter coefficients can be analytically obtained by a simple integration. Our method is to use P wavelets per octave and to approximate them with their oblique projection onto a space defined by a compact scaling function. The wavelet templates ...

We present a purely group-theoretical derivation of the continuous wavelet transform (CWT) on the (n ? 1)-sphere S n?1 , based on the construction of general coherent states associated to square integrable group representations. The parameter space of the CWT, Y SO(n)R + , is embedded into the generalized Lorentz group SO o (n; 1) via the Iwasawa decomposition, so that X ' SO o (n; 1)=N, where ...