Heisenberg's uncertainty principle for N-dimensional fractional Fourier transform of complex-valued functions

被引：6

作者：

Zhang, Zhi-Chao ^{[1
,2
]}

Han, Pu-Yu ^{[1
]}

Sun, Yun ^{[1
]}

Wu, An-Yang ^{[1
]}

Shi, Xi-Ya ^{[1
]}

Qiang, Sheng-Zhou ^{[1
]}

Jiang, Xian ^{[1
]}

Wang, Ga ^{[3
]}

Liu, Lu-Bo ^{[4
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Jiangsu, Peoples R China

[2] Macau Univ Sci & Technol, Fac Informat Technol, Macau 999078, Peoples R China

[3] Nanjing Res Inst Elect Technol, Nanjing 210039, Jiangsu, Peoples R China

[4] Southwest Inst Elect Technol China, Chengdu 610036, Sichuan, Peoples R China

来源：

OPTIK | 2021年 / 242卷

基金：

中国国家自然科学基金;

关键词：

Complex-valued function; Fractional Fourier transform; N-dimensional Heisenberg's uncertainty principle; Optical systems analysis; Time-frequency analysis; IMPLEMENTATION;

D O I：

10.1016/j.ijleo.2021.167052

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

The latest N-dimensional Heisenberg's uncertainty principle associated with complex-valued functions' uncertainty product in the Fourier transform domain is extended into two fractional Fourier transform (FRFT) domains. The result derived is sharper than the existing ones in the literature, giving rise to a tighter lower bound on the uncertainty product in time and N-dimensional FRFT domains, as well as that in two N-dimensional FRFT domains. Example and simulations also validate the correctness of theoretical analyses, and finally the effectiveness is illustrated by applications in the effective estimation of spreads in time-frequency analysis and optical systems analysis.

引用

页数：9