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

• Published in: Signal processing 2023-03, Vol.204, p.108836, Article 108836
• Main Authors: Raposo–Sánchez, Miguel Ángel, Sáez–Landete, José, Cruz–Roldán, Fernando
• Format: Article
• Language: English
• Subjects: [formula omitted] and [formula omitted]spline functions; Convolution; Filtering theory; FIR digital filters; Principally flat filters
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2022.108836

•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. 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.