On computation of the discrete W transform

This article presents new fast algorithms for the type-II, -III, and -IV discrete W transform (DWT). The type-II and -III DWT is decomposed into two length-N/2 type-I DWTs, and the type-IV is converted into two length-N/2, type-II or type-III DWTs. The proposed algorithms achieve a simple computational structure and naturally support a wide range of sequence lengths. Savings on the number of arithmetic operations are achieved for the type-II to -IV DWT when N=15*2/sup r/.