In this paper the second generation wavelets are applied as a basis in finite element method. The wavelet basis is constructed over typical nonequispaced nodes and on boundaries. In addition the wavelet bases are tailored to the Poisson's operator. The wavelet basis is lifted to enforce operator orthogonality, this eliminates coupling between coarse and detail parts of the stiffness matrix. The...

This paper shows that the naturally induced discrete diierentia-tion operators induced from a wavelet-Galerkin nite-dimensional approximation to a standard function space approximates diierentiation with an error of order O(h 2d+2), where d is the degree of the wavelet system. The degree of a wavelet system is deened as one less than the degree of the lowest order non-vanishing moment of the fu...

We show that a multi-dimensional scaling function of order γ (possibly fractional) can always be represented as the convolution of a polyharmonic B-spline of order γ and a distribution with a bounded Fourier transform which has neither order nor smoothness. The presence of the B-spline convolution factor explains all key wavelet properties: order of approximation, reproduction of polynomials, v...

This paper shows that the naturally induced discrete differentiation operators induced from a wavelet-Galerkin finite-dimensional approximation to a standard function space approximates differentiation with an error of order 0(h2d+2), where d is the degree of the wavelet system. The degree of a wavelet system is defined as one less than the degree of the lowest-order nonvanishing moment of the ...

This paper explains a study conducted based on wavelet packet transform techniques. In this paper the key idea underlying the construction of wavelet packet analysis (WPA) with various wavelet basis sets is elaborated. Since wavelet packet decomposition can provide more precise frequency resolution than wavelet decomposition the implementation of one dimensional wavelet packet transform and the...

Extended Abstract Wavelet packets 14] represent a generalization of the method of multires-olution decomposition and comprise the entire family of subband coded (tree) decompositions 11, 15]. Whereas in the wavelet case the decomposition is applied recursively to the coarse scale approximations (leading to the well known (pyramidal) wavelet decomposition tree), in the wavelet packet decompositi...

Corresponding Author: Fikri Budiman Department of Computer Science, University of Dian Nuswantoro, Semarang, Indonesia Email: [email protected] Abstract: Image retrieval using Support Vector Machine (SVM) classification very depends on kernel function and parameter. Kernel function used by dot product substitution from old dimension feature to new dimension depends on image dataset ...

this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...

This paper deals with time series of monthly sardines catches in the north area of Chile. The proposed method combines radial basis function neural network (RBFNN) with wavelet denoising algorithm. Wavelet denoising is based on stationary wavelet transform with hard thresholding rule and the RBFNN architecture is composed of linear and nonlinear weights, which are estimated by using the separab...

Recognition of the presence of any power disturbance and classifying any existing disturbance into a particular type is the first step in combating the power quality problem. In spite of the extensive number of power disturbances classification methods, a research on the selection of useful features from the existing feature set and the parameter optimization for specific classifiers was omitte...