Generalized coiflet systems

Ingrid Daubechies (1990) showed that setting moments of the wavelets to zero increased the smoothness of the scaling functions and wavelets in a wavelet basis system. Later she constructed wavelet systems with both zero scaling function and wavelet moments called "coiflets" after Ronold Coifman who first suggested this strategy. This paper generalizes the definition of the coiflet to allow approximately equal numbers of zero scaling function and wavelet moments. This results in the partitioning of the systems into three classes, each with well defined characteristics. We also discover that these systems have more zero moments than the available degrees of freedom would predict and that the solutions to the requirements are not unique.