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 suppo rt width. Ii: is known how to design biorthogonal coiflets with ddd-length filters. However, the precise relationship among the vanishing moments of t he analysis and synthesis scaling functions is unknown, This is the first p roblem solved in this correspondence. Second, biorthogonal coiflets with ev en-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 ad vanced. Each of these two wavelet families is parametrized by three integer s. The design is based on explicit formulae.