A method of decomposing wavelets filters into lifting steps by solving equations

The lifting scheme provides us a powerful tool for constructing biorthogonal wavelets. Meanwhile, it is a new explanation of first generation wavelets, i.e., any first generation wavelets filter can be decomposed into some lifting steps. A method of decomposing biorthogonal wavelets filters into lifting steps by solving equations is presented in this paper. The lifting coefficients can be obtained by solving the equations directly. Without repeating Euclid algorithm, our method is more efficient. It works well and has the same result with existing methods.