Piecewise-Polynomial HAAR Wavelets And Their Application

Аннотация

This article presents piecewise polynomial Haar wavelets and shows that they can be used to interpolate functions and signals. An algorithm for interpolating functions in the wavelet bases on piecewise constant and piecewise linear Haar functions developing, and the results of estimating interpolation errors are also presented. It is shown that when interpolating using piecewise constant Haar wavelets, the error will increase sharply, to reduce the error, it is recommended to use piecewise linear Haar wavelets and as a result, an error reduction is achieved.