This study applies the RBF wavelet series to the evaluation of analytical solutions of linear time-dependent wave and diffusion problems of any dimensionality and geometry. To the best of the author’s knowledge, such analytical solutions have never been achieved before. The RBF wavelets can be understood an alternative for multidimensional problems to the standard Fourier series via fundamental...

Alternative ways to represent speaker’s voice individuality are studied for the task of speaker verification. We exploit a set of orthonormal bases provided by wavelet packets that allow an effective manipulation of the frequency subbands according to the critical bands concept. Novel wavelet packet based sets of speech features are contrasted with existing wavelet features as well as with the ...

A biorthogonal wavelet is derived from a pair of biorthogonal refinable functions using the standard technique in multiresolution analysis. In this paper, we introduce the concept of projectable refinable functions and demonstrate that many multivariate refinable functions are projectable; that is, they essentially carry the tensor product (separable) structure though themselves may be non-tens...

In this paper, a novel wavelet balance method is proposed for steady-state analysis of nonlinear circuits. The proposed method presents several merits compared with those conventional frequency domain techniques. First, it has a high convergence rate. Second, it works in time domain so that many critical problems in frequency domain can be handled efficiently. Third, an adaptive scheme exists t...

In this paper, we study the properties of the transform which approximates a signal at a given resolution. We show that the difference of a signal at different resolutions can be extracted by decomposing the signal on a wavelet orthonormal basis. In wavelet orthonormal basis is a family of functions, which is built by dilating and translating a unique function. The development of orthonormal wa...

We take advantage of ideas of an orthogonal wavelet complement to produce multiresolution orthogonal decomposition of nonuniform Bspline (NUB) spaces. The editing of NUB curves and surfaces can be handled at different levels of resolutions. Applying Multiresolution decomposition to possiblyC1 discontinuous surfaces, one can preserve the general shape on one hand and local features on the other ...

We consider the problem of estimating an unknown function f in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis {ψjk(G), j, k} warped with the design. This allows to perform a very stable and computable thresholding algorithm. We investigate the properties of this new basis. In particular, we prove that if the desig...

The so-called denoising problem, relative to normal models for noise, is formalized such that`noise' is deened as the incompressible part in the data while the compressible part deenes the meaningful information bearing signal. Such a decomposition is eeected by minimization of the ideal code length, called for by the Minimum Description Length (MDL) principle, and obtained by an application of...

In an attempt to find out a more appropriate representation of a speech signal for the task of speaker recognition, we study alternative ways to represent speakers’ voices individuality. A novel wavelet packet based set of speech features, apposite for speaker recognition, is proposed. We exploit the capabilities offered by the plethora of existing wavelets, along with the powerful set of ortho...

Corrosion causes a degradation of the structural integrity of petrochemical plants, nuclear power plants, ships, bridges and other constructions containing steel with the 29 consequence that people and the environment may be exposed to dangerous situations. The detection of corrosion and the prediction of the type of corrosion are studied in this 31 article by means of the acoustic emission tec...