Biorthogonal coiflets

Coiflets are filter banks, where the sum of the number of vanishing moments of the analysis and synthesis limit functions is maximum for a given support width. It is known how to design biorthogonal coiflets with odd-length filters. However, the precise relationship among the vanishing moments of the analysis and synthesis scaling functions is unknown. This is the first problem solved in this correspondence. Second, biorthogonal coiflets with even length filters, which have remained unknown previously, are designed and the relationship among the vanishing moments of the analysis and synthesis limit functions shown. A generalization of the Bernstein polynomial is advanced. Each of these two wavelet families is parametrized by three integers. The design is based on explicit formulae