Uncertainty principles for the short-time linear canonical transform of complex signals

被引:32
作者
Gao, Wen-Biao [1 ,2 ]
Li, Bing-Zhao [1 ,2 ]
机构
[1] Beijing Inst Technol, Sch Math & Stat, Beijing 102488, Peoples R China
[2] Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 102488, Peoples R China
基金
中国国家自然科学基金;
关键词
Linear canonical transform; Short-time linear canonical transform; Complex signal; Uncertainty principle;
D O I
10.1016/j.dsp.2020.102953
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
The short-time linear canonical transform (STLCT) is a novel time-frequency analysis tool. In this paper, we generalize some different uncertainty principles for the STLCT of complex signals. Firstly, a new uncertainty principle for STLCT of complex signals in time and frequency domains is explored. Secondly, an uncertainty principle in two STLCT domains is obtained. They show that the lower bounds are related to the covariance of time and frequency and can be achieved by complex chirp signals with Gaussian signals. Then the uncertainty principle for the two conditional standard deviations of the spectrogram associated with the STLCT is derived. In addition, an example is also carried out to verify the correctness of the theoretical analyses. Finally, some potential applications are presented to show the effectiveness of the theorems. (C) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页数:10
相关论文
共 48 条
[1]   Some properties of windowed linear canonical transform and its logarithmic uncertainty principle [J].
Bahri, Mawardi ;
Ashino, Ryuichi .
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2016, 14 (03)
[2]   Optimal filtering with linear canonical transformations [J].
Barshan, B ;
Kutay, MA ;
Ozaktas, HM .
OPTICS COMMUNICATIONS, 1997, 135 (1-3) :32-36
[3]   Logarithmic Uncertainty Relations for Odd or Even Signals Associate with Wigner-Ville Distribution [J].
Cao, Yu-Jing ;
Li, Bing-Zhao ;
Li, Yong-Gang ;
Chen, Yi-Hong .
CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2016, 35 (07) :2471-2486
[4]  
Cohen L, 2001, APPL NUM HARM ANAL, P217
[5]  
COHEN L, 1995, P SOC PHOTO-OPT INS, V2563, P80, DOI 10.1117/12.211427
[6]  
Cohen L., 1995, TIME FREQUENCY ANAL
[7]  
Cohen L., 1994, IEEE SP INT S TIM FR
[8]   A Tighter Uncertainty Principle for Linear Canonical Transform in Terms of Phase Derivative [J].
Dang, Pei ;
Deng, Guan-Tie ;
Qian, Tao .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2013, 61 (21) :5153-5164
[9]  
Debnath L., 2015, Integral transforms and their applications, Vthird
[10]   INFORMATION THEORETIC INEQUALITIES [J].
DEMBO, A ;
COVER, TM ;
THOMAS, JA .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (06) :1501-1518