Generalized coiflets: a new family of orthonormal wavelets

We generalize an existing family of wavelets, coiflets, by replacing the zero-centered vanishing moment condition on scaling functions by a nonzero-centered one in order to obtain a novel class of compactly supported orthonormal wavelets (we call them generalized coiflets). This generalization offers an additional free parameter i.e., the center of mass of the scaling function, which can be tuned to obtain improved characteristics of the resulting wavelet system such as near-symmetry of the scaling functions and wavelets, near-linear phase of the filter banks, and sampling approximation properties. Therefore, these new wavelets are promising in a broad range of applications in signal processing and numerical analysis.