Sampling bases for the signal space composed of spline functions
Masaru Kamada, Kazuo Toraichi, Ryoichi Mori · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1989
Abstract The signal space composed of spline functions, which are smooth piecewise polynomials and almost free from oscillation, has attracted attention in the problems of interpolation and signal approximation. to make full use of such a signal space, there must be available a clear description of its properties. As a general approach to this problem, it is effective to derive the sampling basis in the signal space. Previously, the authors discussed the signal space composed of spline functions, and derived the sampling basis for the case where the degree is restricted to two. This paper extends the result to the arbitrary degree. Exam ples of sampling bases are shown for the practical cases of the second and the third degrees. the sampling basis derived in this paper provides the basic characterization of the signal space composed of spline functions of arbitrary degree.