SAMPLING THEOREM FOR SPLINE SIGNAL SPACE OF ARBITRARY DEGREE

作     者：IWAKI, M TORAICHI, K 

作者机构：Univ of Tsukuba Tsukuba-shi Japan 

出 版 物：《IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES》 (IEICE Trans Fund Electron Commun Comput Sci)

年 卷 期：1994年第E77A卷第5期

页      面：810-817页

核心收录：

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：DIGITAL PROCESSING INFORMATION THEORY CODING THEORY SPLINE FUNCTIONS 

摘      要：In the band-limited signal space, the mutual relation between continuous time signal and discrete time signal is expressed by the sampling theorem of Whittaker-Someya-Shannon. This theorem consists of an orthonormal expansion formula using sinc functions. In that formula, the expansion coefficients are identical to the sample values of signals. In general, the band-limited signal space is not always suited to model the signals in nature. The authors have proposed a new model for signal processing based on finite times continuously differentiable functions. This paper aims to complete the sampling theorem for the spline signal spaces, which corresponds to the sampling theorem of Whittaker-Someya-Shannon in the band-limited signal space. Since the obtained sampling theorem gives the simplest representation of signals, it is considered to be the most fundamental characterization of spline functions used for signal processing. The biorthonormal basis derived in this paper is considered to be a system of delta functions at sampling points with some continuous differentiability.