Fractional Splines Wavelets

The fractional splines are an extension of the polynomial splines for all fractional degrees α > -1. Their basic constituents are piecewise power functions of degree α. One constructs the corresponding B-splines through a localization process similar to the classical one, replacing finite differences by fractional differences. The fractional B-splines share virtually all the properties of the classical B-splines, including the two-scale relation, and can therefore be used to define new wavelet bases with a continuously-varying order parameter