Explicit Construction of Framelets

Abstract

We study tight wavelet frames associated with given refinable functions which are obtained with the unitary extension principles. All possible solutions of the corresponding matrix equations are found. It is proved that the problem of the extension may be always solved with two framelets. In particular, if symbols of the refinable functions are polynomials (rational functions), then the corresponding framelets with polynomial (rational) symbols can be found. © 2001 Academic Press.