Multiwavelets with Extra Approximation Properties


Because multiwavelet bases normally lack important properties traditional wavelet bases (of equal approximation order) possess, the discrete multiwavelet transform is less useful for signal processing, unless preceded by a preprocessing step. This paper examines properties of orthogonal multiwavelet bases, with approximation order >1, that possess those properties normally absent. For these ``balanced'' bases (after Lebrun and Vetterli) prefiltering can be avoided. Using results regarding M-band wavelet bases, it has been found that balanced multiwavelet bases can be characterized in terms of the divisibility of certain transfer functions by powers of (z^{-2r}-1)/(z^{-1}-1). The paper also presents a balanced version of the DGHM basis --- the scaling functions are simultaneously symmetric, orthogonal and of compact support.

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