A general framework for sampling and reconstruction in function spaces associated with fractional Fourier transform

作     者：Liu, Xiaoping Shi, Jun Sha, Xuejun Zhang, Naitong 

作者机构：Harbin Inst Technol Commun Res Ctr Harbin 150001 Peoples R China Harbin Inst Technol Shenzhen Grad Sch Shenzhen 518055 Peoples R China 

出 版 物：《SIGNAL PROCESSING》 (信号处理)

年 卷 期：2015年第107卷

页      面：319-326页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 

基　　金：National Basic Research Program of China [2013CB329003] National Natural Science Foundation of China 

主　　题：Fractional Fourier transform Non-bandlimited Function spaces Uniform sampling Signal reconstruction 

摘      要：The fractional Fourier transform (FRET) has proven to be a powerful tool in optics and signal processing. Sampling theory of this transform for band-limited signals has blossomed in recent years. However, real-world signals are often not band-limited. In this paper, we first develop the theory of frames for function spaces associated with the FRFT, then we propose a general framework for FRFT-based sampling and reconstruction in function spaces without band-limiting constraints. Based upon the proposed framework, a simple necessary and sufficient condition for FRFT-based uniform sampling in function spaces is found, which facilitates a straightforward derivation of the uniform sampling theorem for the FRFT. The theoretical derivations are validated by the means of numerical results. (C) 2014 Elsevier B.V. All rights reserved.