Explicit construction of framelets

We study tight wavelet frames associated with given refinable functions whi ch are obtained with the unitary extension principles. All possible solutio ns of the corresponding matrix equations are found. It is proved that the p roblem of the extension may be always solved with two framelets. In particu lar, if symbols of the refinable functions are polynomials (rational functi ons), then the corresponding framelets with polynomial (rational) symbols c an be found. (C) 2001 Academic Press.