Abstract: Using the demonstration about the interpolation of W.Swelden and M.J.Shensa , we prove that the interpolated wavelet tight frame generated by three generators does not exist. Under satisfying nearly interpolation and higher vanishing moment, we design a low-pass filter, and then using an inequality giving by Ron, we will get three high-pass filters. Therefore we can get the wavelet tight frames that satisfy our properties. Two of those high-pass filters satisfy symmetry or antisymmetry, and all of them have a free parameter. The greater freedom will widen the selection of both low-pass and high-pass filters. Finally, we give the algorithm for filters and some concrete examples of wavelet tight frames.

Key words: wavelet tight frame, vanishing moment, symmetry, interpolation