Abstract
Regensburger and Scherzer described a symbolic computation method for moments and filter coefficients of scaling functions and obtained parametrizing compactly supported orthonormal wavelets. Following the idea, we are devoted to a study moments and parameterization construction for 3-band biorthogonal scaling coefficients with several vanishing moments. Firstly, we investigate the relations between filter lengths and symmetry. Then, we prove the relationship between dual continuous moments of 3-band biorthogonal scaling functions in theorem 2. This theorem reveals that the sum of continuous moments of dual scaling functions and is completely determined by the lower discrete moments. And we show the fact that the odd-indexed discrete moments are determined by the smaller even-indexed discrete moments. Finally, a family 3-band biorthogonal scaling coefficients with discrete moments as parameters are explicitly expressed based on computer algebra.
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