Abstract: This paper studies wavelet tight frames associated with given scaling functions with dilatin factor α. The wavelet tight frames consist of
finite number of functions ψ¹,ψ²,...,ψⁿ. First, the authors present sufficient conditions for existence of wavelet tight frames generated by the n functions, then give explicit constructing formula of wavelet tight frames. In particular, if mask of the scaling function are rational functions, the mask of the corresponding wavelet tight frames are rational. Finally, the paper derive the decomposition and reconstruction formulas, and give five numercial examples of wavelet tight frames.

Key words: Wavelet tight frame, Frames multiresolution analysis, Scaling function,
Decomposition, Reconstruction