Piecewise‐quadratic Harmut basis functions and their application to problems in digital signal processing

Abstract

SUMMARYIn this work, the well-known system of orthogonal piecewise-constant Harmut basis functions is investigated. As a result of research, their shortcomings are revealed such as weak convergence, discontinuity and others. To eliminate these problems, a new basis of piecewise-quadratic Harmut functions is proposed and a fast spectral transformation algorithm is developed in this basis. For examples of analytically set and experimentally verified dependencies, the advantages of the algorithm for spectral transformations in a basis of piecewise-quadratic Harmut functions are demonstrated. The proposed system and algorithm could find wide application in such areas as computer graphics, image processing and restoration, machine vision and multimedia, animation and programming of computer games.

Development of the Method, Algorithm and Software of a Modern Non-invasive Biopotential Meter System

“…In order to obtain adequate bio potential signals, intimate small skin-sensor contact is required. For this purpose, the current state of the development of non-invasive bio-measuring devices has been analyzed and the problems of creating computer bio-measuring devices have been revealed [12][13][14][15][16][17].…”

Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point

“…The Chebyshev differentiation matrix is used to find the approximate solutionŜ(x) of ODE (6). If Θ(x) is any phase function of integral (1) such that Θ (x) = 0 for all x ∈ [a, b], then the discretized form of the ODE (6) at Chebyshev-Gauss-Lobatto nodes is given bŷ…”

“…In the last two decades, a number of accurate and efficient methods have been designed for numerical evaluation of one-dimensional highly oscillatory integrals, which include: the asymptotic method [5][6][7][8], the numerical steepest descent method [9], the Filon(-type) methods [10,11], and the Levin(-type) methods [12][13][14][15][16]. Among which, the Levin method has attracted much attention as it can handle highly oscillatory integrals with complicated phase functions.…”