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(Nlog₂N/log₂log₂N) and is superior to the O(Nlog₂N) in the conventional DWT. The proposed algorithm achieves a simple computational structure and naturally deals with any sequence lengths.