We discuss here wavelets constructed from periodic spline functions. Our approach is based on a new computational technique named Spline Harmonic Analysis (SHA). SHA to be presented is a version of harmonic analysis operating in the spaces of periodic splines of defect 1 with equidistant nodes. Discrete Fourier Transform is a special case of SHA. The continuous Fourier Analysis is the limit cas...

Ringing, the high-frequency response of a structure to relatively low-frequency waves, has been a great concern in offshore engineering. To investigate this phenomenon, we solve the third-harmonic diffraction problem using a three-dimensional higher-order panel method in the low-frequency range. In this thesis, the boundary integral equations are derived from two different theories , based on c...

This paper addresses the problem of spherical parametrization, i.e., mapping a given polygonal surface of genus-zero onto a unit sphere. We construct an improved algorithm for parametrization of genus-zero meshes and aim to obtain high-quality surfaces fitting with PHT-splines. This parametrization consists of minimizing discrete harmonic energy subject to spherical constraints and solving the ...

Spiine, periodic spline and spherical harmonic maximum reach estimation procedures are compared and evaluated based on ease of usage, estimation error and bias. The comparison indicates that each method provides comparable estimates based on percent variance accounted for (Rz) and standard error. Spherical harmonics, however, are less biased and provide accurate estimates of the maximum reach s...

Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions. RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids. Despite these fundamental differences, we show that the two types of representation are closely linked together . . . through fractals. First, we iden...

For certain classes of fractal differential equations on the Sierpinski gasket, built using the Kigami Laplacian, we describe how to approximate solutions using the finite element method based on piecewise harmonic or piecewise biharmonic splines. We give theoretical error estimates, and compare these with experimental data obtained using a computer implementation of the method (available at th...

An innovatory on–line method of power system frequency estimation and voltage/current signals resampling is presented. The method is designed to increase the accuracy of power system equivalent harmonic impedance estimation using simple DAQ systems. Estimation of instantaneous frequency uses 5–th degree polynomial interpolation of filtered signal zero crossings time positions. Final resampling ...