Novel uncertainty relations associated with fractional Fourier transform  

作　　者：徐冠雷 王孝通 徐晓刚 

机构地区：[1]Department of Navigation,Dalian Naval Academy [2]Institute of Photoelectric Technology [3]Department of Automatization,Dalian Naval Academy

出　　处：《Chinese Physics B》2010年第1期294-302,共9页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No. 60473141);the Natural Science Foundation of Liaoning Province of China (Grant No. 20062191)

摘　　要：In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special ease of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains.In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special ease of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains.

关 键 词：fractional Fourier transform （FRFT） uncertainty principle time-frequency spreads group delay 

分 类 号：O174.22[理学—数学]