A note on connection between spline signal spaces and band‐limited signal spaces
Kazuo Toraichi, Masaru Kamadas · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1991
Abstract If the signal space matched to the representation is selected according to the properties of the signal to be handled, the signal processing can be made efficient. This paper is a step toward the structuralization of the signal spaces for systematic selection of the signal space. As a particular problem, the relation is analyzed between the signal spaces composed of spline functions, which have the feature that the smoothness as the continuous differentiability varies according to the degree, and the band‐limited signal spaces, which is fundamental in the signal processing. As a result of analysis, it is shown that the signal spaces composed of spline functions agree with the band‐limited signal spaces in the limit of infinite order. This implies that the signal spaces composed of spline functions and the band‐limited signal spaces can be structured as a sequence with the degree as the parameter. The result in this paper provides a view that the continuous differentiability can be used as an index in the systematic selection of the signal spaces.