Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform

Atanasova, Sanja; Maksimović, Snježana; Pilipović, Stevan

doi:10.3390/axioms10040240

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2023

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“…The windowed linear canonical transform (WLCT) [9][10][11] is a generalized integral transform of the FT [12] and the FRFT [13]. In recent years, inequality of the WLCT has become a hot topic.…”

Section: Introductionmentioning

confidence: 99%

Inequalities for the Windowed Linear Canonical Transform of Complex Functions

Gao

2023

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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.

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