Inequalities for the Windowed Linear Canonical Transform of Complex Functions

被引：2

作者：

Li, Zhen-Wei ^{[1
]}

Gao, Wen-Biao ^{[2
]}

机构：

[1] Wuhan Text Univ, Sch Comp Sci & Artificial Intelligence, Wuhan 430073, Peoples R China

[2] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Peoples R China

来源：

AXIOMS | 2023年 / 12卷 / 06期

关键词：

Fourier transform; linear canonical transform; inequality; complex function; UNCERTAINTY PRINCIPLE; FOURIER-TRANSFORM; THEOREMS;

D O I：

10.3390/axioms12060554

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we generalize the N-dimensional Heisenberg's inequalities for the windowed linear canonical transform (WLCT) of a complex function. Firstly, the definition for N-dimensional WLCT of a complex function is given. In addition, the N-dimensional Heisenberg's inequality for the linear canonical transform (LCT) is derived. It shows that the lower bound is related to the covariance and can be achieved by a complex chirp function with a Gaussian function. Finally, the N-dimensional Heisenberg's inequality for the WLCT is exploited. In special cases, its corollary can be obtained.

引用

页数：10

共 23 条

[1]

[Anonymous], 2013, Linear Canonical Transform and Its Applications

[2]

[Anonymous], 2009, Fractional Fourier Transform and Its Applications

[3] Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform [J].

Atanasova, Sanja ;

Maksimovic, Snjezana ;

Pilipovic, Stevan .

AXIOMS, 2021, 10 (04)

[4] 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)

[5] 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

[6] Pitt inequalities and restriction theorems for the Fourier transform [J].

De Carli, Laura ;

Gorbachev, Dmitry ;

Tikhonov, Sergey .

REVISTA MATEMATICA IBEROAMERICANA, 2017, 33 (03) :789-808

[7] Octonion Short-Time Fourier Transform for Time-Frequency Representation and Its Applications [J].

Gao, Wen-Biao ;

Li, Bing-Zhao .

IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2021, 69 :6386-6398

[8] Uncertainty principles for the short-time linear canonical transform of complex signals [J].

Gao, Wen-Biao ;

Li, Bing-Zhao .

DIGITAL SIGNAL PROCESSING, 2021, 111

[9] Quaternion Windowed Linear Canonical Transform of Two-Dimensional Signals [J].

Gao, Wen-Biao ;

Li, Bing-Zhao .

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2020, 30 (01)

[10] Convolution theorem involving n-dimensional windowed fractional Fourier transform [J].

Gao, Wenbiao ;

Li, Bingzhao .

SCIENCE CHINA-INFORMATION SCIENCES, 2021, 64 (06)

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