Discrete orthogonal M-band wavelet decompositions

The authors generalize the discrete orthogonal two-band (or dyadic) wavelet decomposition to the M-band case. Specifically, it is shown that any finite energy signal can be explained in terms of the dilates and translates of M-1 M-band wavelets. The advantage of such decompositions is that they are much more compact than two-band wavelet decompositions. This compactness is important both in coding applications and for the development of fast signal processing algorithms. A complete characterization of discrete orthogonal M-band wavelets is given, including a recipe for constructing such wavelets