Multiwavelet bases with extra approximation properties

This paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order. Because multiwavelet bases normally lack important properties that traditional wavelet bases (of equal approximation order) possess, the associated discrete multiwavelet transform is less useful for signal processing unless preceded by a preprocessing step (preflltering). This paper examines the properties and design of orthogonal multiwavelet bases with approximation order > 1 that possess those properties that are normally absent. For these balanced bases (so named by Lebrun and Vetterli), prefltering can be avoided. By reorganizing the multiwavelet (vector) filter bank as a multichannel scalar filter bank, the development in this paper draws from results regarding the approximation order of M-band wavelet bases. A main result thereby obtained is a characterization of balanced multiwavelet bases in terms of the divisibility of certain transfer functions by 0~2r - i)/(z-1 - 1).