Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles-Reference-Cited by-同舟云学术

Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles

Published:2022-01-03 Issue:1 Volume:2022 Page:
ISSN:1029-242X
Container-title:Journal of Inequalities and Applications
language:en
Short-container-title:J Inequal Appl

Author:

Bahri Mawardi

Abstract

AbstractThe windowed linear canonical transform is a natural extension of the classical windowed Fourier transform using the linear canonical transform. In the current work, we first remind the reader about the relation between the windowed linear canonical transform and windowed Fourier transform. It is shown that useful relation enables us to provide different proofs of some properties of the windowed linear canonical transform, such as the orthogonality relation, inversion theorem, and complex conjugation. Lastly, we demonstrate some new results concerning several generalizations of the uncertainty principles associated with this transformation.

Funder

Universitas Hasanuddin

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Link

https://link.springer.com/content/pdf/10.1186/s13660-021-02737-1.pdf

Reference21 articles.

1. Bai, R.F., Li, B.Z., Cheng, Q.Y.: Wigner–Ville distribution associated with the linear canonical transform. J. Appl. Math. 2012, Article ID 740161 (2012)

2. Che, T.W., Li, B.Z., Xu, T.Z.: Ambiguity function associated with the linear canonical transform. EURASIP J. Adv. Signal Process. 138, 1–14 (2012)

3. Bahri, M., Ashino, R.: Convolution and correlation theorems for Wigner–Ville distribution associated with linear canonical transform. In: 12th International Conference on Information Technology-New Generations, Las Vegas, NV, USA (2015)

4. Bahri, M., Karim, S.A.A.: On relationship between ambiguity function and linear canonical ambiguity function. In: Karim, S.A.A., Shafie, A. (eds.) Towards Intelligent Systems Modeling and Simulation. Springer, Cham (2022)

5. Kou, K.I., Xu, R.H., Zhang, Y.H.: Paley–Wiener theorems and uncertainty principles for the windowed linear canonical transform. Math. Methods Appl. Sci. 35, 2122–2132 (2012)

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Various generalizations of uncertainty principles related to the linear canonical ambiguity function;Journal of Mathematics and Computer Science;2024-05-09

2. Uncertainty principles for coupled fractional Wigner–Ville distribution;Royal Society Open Science;2024-05

3. Uncertainty principles for windowed coupled fractional Fourier transform;Mathematical Methods in the Applied Sciences;2024-02-23

4. Short-time free metaplectic transform: Its relation to short-time Fourier transform in $ L^2(\mathbb R^n) $ and uncertainty principles;AIMS Mathematics;2023