Fast discrete W transforms via computation of moments

A novel approach to compute all four types of Discrete W transform (DWT) is proposed. By using kernel transforms and Taylor expansions, a DWT is approximated by a linear sum of discrete moments. This enables us to use computational techniques developed for computing moments to compute DWTs efficiently. The amount of multiplications used in our method is O(N log(2) N/ log(2) log(2) N) and is superior to the O(N log(2) N) in the conventional DWT. The proposed algorithm achieves a simple computational structure and naturally deals with any sequence lengths.