A wavelet system is a collection of the form
. A wavelet is said to be MRA-based if there exists a multiresolution analysis such that
is a frame, we call its elements framelets. The authors present the unitary extension principle and the oblique extension principle to facilitate constructions of MRA-based tight wavelet frames. Approximation orders and vanishing moments of MRA-based wavelet systems are studied in order to construct framelets with higher approximation orders. The scaling functions of these framelets are pseudo-splines, i.e., square roots of
. Fast implementation algorithms are also provided.