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

Abstract

α−spline functions, which are a generalization of conventional B−splines, are defined with several parameters which provide more flexibility in terms of the variety of shapes that the functions can adopt. Because of this feature, the α−spline functions have shown improvements in the performance of several applications, including the design of digital filters. This article proposes a novel parametrization to generate new families of α−spline functions that allows a more efficient control of the shape of these functions. Different combinations of parameters are presented, and a detailed analysis of the properties of the new functions is carried out. In addition, the new α−spline functions are applied to the design of digital filters, providing an appropriate design procedure. The characteristics of the new filters are analysed and compared with previous design techniques, demonstrating the remarkable superiority of their performance.