Fast algorithms for computing the discrete W transforms
S. C. Chan, K.L. Ho · 2002
New algorithms for computing the discrete W transform (DWT) of arbitrary lengths are presented. It is found that an odd length type II and III DWT can be mapped to a discrete Hartley transform (DHT) by means of a simple index mapping. The DHT or DWT-I can be computed, for example, by the real-valued fast Fourier transform algorithms such as the real-valued prime factor fast Fourier transform algorithm (RPFA FFT). Using the close relationship between the odd DFTs and the DWTs, it is possible to compute the type II and III DWTs with even lengths by means of the real-valued FFT or the fast Hartley transform (FHT). Similar algorithms are also presented for the DWT-IV.>