A novel parametrization of α-spline functions: Application to digital filter design

•A novel parametrization to generate four different families of α-spline functions is proposed.•The proposed new formulation allows more precise control to set the shape of the function, and it can be applied to different fields of signal processing.•It is also derived a new mathematical polynomial form of the alpha-spline functions, since it helps to obtain and analyze closed expressions without resorting to numerical approximations.•The new polynomial form allows to impose conditions on their continuity and derivability that are useful in certain applications (e.g., filtering). Some properties of the α-spline functions are also derived.•As a case study example of the possible applications of the new families of α-splines, their application to digital filter design is presented, and their quality is analyzed using standard metrics and compared with other techniques previously reported in the literature.