On computation of the discrete W transform

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