This paper proposes a new correlation analysis method for nonstationary and energy-limited continual signals, which works out a formula similar to time correlation theory; that is to say when the operator, , meets a certain condition, its auto-correlation property of Fourier transform can be presented by Fourier transform of its energy function, f 2 ) ( t f , revealing its correlation of the Fo...

This article develops a wavelet decomposition of a stochastic process which parallels a time{localized Cram er (Fourier) spectral representation. We provide a time{scale instead of a time{frequency decomposition and, hence, instead of thinking as scale in terms of \inverse frequency" we start from genuine time{scale building blocks or \atoms". Using this class of locally stationary wavelet (LSW...

The main aim of this dissertation is to study the topic of wavelet neural networks and see how they are useful for dynamical systems applications such as predicting chaotic time series and nonlinear noise reduction. To do this, the theory of wavelets has been studied in the first chapter, with the emphasis being on discrete wavelets. The theory of neural networks and its current applications in...

This thesis describes a set of tools for manipulating sampled signals using wavelet transforms, and outlines potential musical applications of this library. Wavelets improve on existing time frequency methods by representing signals as a sum of a single wavelet basis function at different positions and scales. A wavelet representation can be used to synthesize or transform sounds in a variety o...

Over the last years, wavelet theory has been used with great success in a wide range of applications as signal denoising and image compression. An ideal image compression system must yield high-quality compressed image with high compression ratio. This paper attempts to find the most useful wavelet function to compress an image among the existing members of wavelet families. Our idea is that a ...

Various results on constructing wavelets, multiwavelets and wavelet frames for periodic functions are reviewed. The orthonormal and Riesz bases as well as frames are constructed from sequences of subspaces called multiresolution analyses. These studies employ general frequency-based approaches facilitated by functions known as orthogonal splines and polyphase splines. While the focus is on the ...

In both applications and wavelet theory, the spline wavelets are especially interesting, in part because of their simple structure. In a previous paper we proved that the function m;l is an m th order spline wavelet having an l th order spline dual wavelet. This enabled us to derive biorthogonal spline wavelet bases. In this paper we rst study the general structure of cardinal spline wavelets, ...

A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface wavelet is obtained by defining fractal surfaces on foldable figures, which tesselate the embedding space by reflections in their bounding hyperplanes instead o...

Abstract: In a power system, the analysis of transient signals is the theoretical basis of fault diagnosis and transient protection theory. Shannon wavelet entropy (SWE) and Shannon wavelet packet entropy (SWPE) are powerful mathematics tools for transient signal analysis. Combined with the recent achievements regarding SWE and SWPE, their applications are summarized in feature extraction of tr...

We present multiscale description of hydrodynamic turbulence in incompressible fluid based on continuous wavelet transform. The wavelet transform of the velocity field is taken in L 1 norm, so that the wavelet coefficients u l (x) have the meaning of the velocity fluctuations of scale l. An extra contribution to the energy transfer from large to smaller scales is derived. It is shown that the K...