Article
Engineering, Electrical & Electronic
Younis Ahmad Bhat, Neyaz A. Sheikh
Summary: In this article, the concept of the windowed octonion Fourier transform (WOFT) is introduced, where the octonion-valued function serves as the window function for square integrable octonion-valued functions on R-3. Various properties of the WOFT, such as left linearity, parity, specific shift, inversion, orthogonality, and Hausdorff-Young inequality, are established. Towards the end of the paper, Pitt's inequality and uncertainty principle for the proposed transform are derived, with potential applications included to demonstrate its effectiveness.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Physics, Multidisciplinary
Haiting Yin, Dayong Lu, Rui Zhang
Summary: This study focuses on the windowed Fourier transform in classical information processing, introducing the concept of quantum window state and proving its applicability to quantum Fourier transform. By proposing the quantum windowed Fourier transform, the quantum Fourier transform is successfully applied to quantum signal processing.
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Tieyu Zhao, Yingying Chi
Summary: This paper proposes a new reformulation of the weighted fractional Fourier transform (WFRFT) to realize quantum FRFT, which can be applied to other transformations. The authors also extend the design to the weighted fractional Hartley transform (WFRHT) and the general weighted fractional-order transform (WFRT). The quantum circuits for WFRFT, WFRHT, and WFRT are designed using quantum Fourier transform and quantum phase estimation. This research provides valuable reference for the design and application of quantum algorithms.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Tieyu Zhao, Yingying Chi
Summary: In this paper, the authors utilize quantum Fourier transform and quantum phase estimation to achieve quantum fractional Fourier transform, and establish the relationship between quantum fractional Fourier transform and a classical algorithm. The flaws in the definitions of multi-fractional Fourier transform are observed, and the circuit of quantum fractional Fourier transform and the reasons for the observed defects are analyzed.
FRACTAL AND FRACTIONAL
(2023)
Article
Engineering, Electrical & Electronic
Fang-Jia Yan, Bing-Zhao Li
Summary: This paper addresses a key challenge in graph signal processing by proposing the windowed graph fractional Fourier transform (WGFRFT) and a fast algorithm for it. The robustness and superiority of the algorithm are verified through simulations, demonstrating its practicality in graph clustering applications.
DIGITAL SIGNAL PROCESSING
(2021)
Article
Mathematics, Applied
Eduardo Bayro-Corrachono, Zuleima Vazquez-Flores
Summary: There is increasing interest in quantum image processing (QIP) to improve classical techniques and their applications using quantum computing properties. Quaternions have been widely used since Hamilton introduced them in 1843. This study demonstrates the use of quantum states and operators in the quaternion field and proposes a novel algorithm for the quantum quaternion Fourier transform (QQFT). The study also explains the limitations of using convolution in quantum image processing and introduces filters such as edge detectors and quantum median filters in the quaternion Fourier spectrum and space domain.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Multidisciplinary Sciences
Mohammad Younus Bhat, Aamir Hamid Dar, Irfan Nurhidayat, Sandra Pinelas
Summary: In this paper, we investigate the (two sided) quaternion windowed quadratic-phase Fourier transform (QWQPFT) and its relation with quaternion Fourier transform (QFT), exploring properties and uncertainty principles associated with QWQPFT.
Article
Mathematics, Applied
Zhen-Wei Li, Wen-Biao Gao
Summary: In this paper, we extend the N-dimensional Heisenberg's inequalities to the windowed linear canonical transform (WLCT) of a complex function. We first provide the definition for N-dimensional WLCT of a complex function. Moreover, we derive the N-dimensional Heisenberg's inequality for the linear canonical transform (LCT), which shows that the lower bound is related to the covariance and can be achieved by a complex chirp function with a Gaussian function. Finally, we explore the N-dimensional Heisenberg's inequality for the WLCT and obtain its corollary in special cases.
Article
Optics
Qingyue Zhang, Yue Su, Rui Li
Summary: This paper discusses the problem of phase retrieval in the discrete windowed special affine Fourier transform domain and provides some appropriate conditions for phase retrieval. The results of numerical simulations validate the theoretical analysis and suggest directions for future work.
Article
Mathematics
Tieyu Zhao, Tianyu Yang, Yingying Chi
Summary: This paper introduces the quantum weighted fractional Fourier transform (QWFRFT), opening up new possibilities for quantum signal processing implementations.
Article
Computer Science, Information Systems
Xianwei Zheng, Cuiming Zou, Li Dong, Jiantao Zhou
Summary: This paper introduces the use of multi-windowed graph Fourier transforms for vertex frequency analysis, efficiently constructing tight graph Fourier frames for different application scenarios and proposing methods for reconstructing graph signals. Experimental results demonstrate successful extraction of vertex frequency features and detection of anomaly data using the proposed methods.
COMPUTER COMMUNICATIONS
(2021)
Article
Engineering, Multidisciplinary
Dan Wu, Lei Qian, Pengfei Zhu
Summary: This paper proposed an image distortion elimination method based on optimized windowed Fourier transform processing. By conducting simulation testing, the optimal parameters were determined and used to successfully calibrate the image distortion of an optical microscope under various magnifications.
PRECISION ENGINEERING-JOURNAL OF THE INTERNATIONAL SOCIETIES FOR PRECISION ENGINEERING AND NANOTECHNOLOGY
(2021)
Article
Engineering, Electrical & Electronic
Wen-Biao Gao, Bing-Zhao Li
Summary: This paper investigates the quaternion windowed linear canonical transform (QWLCT) and explores the uncertainty principles associated with it. Various properties and inequalities of the QWLCT are presented, followed by a study of different uncertainty principles. Finally, a numerical example and a potential application to signal recovery using the uncertainty principle associated with the QWLCT are provided.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Optics
Shikha Sharma, Rishikesh Kulkarni
Summary: This study proposes a spatial carrier fringe demodulation technique based on a state-space modeling approach for phase estimation. By simultaneously estimating the fringe background intensity, carrier frequency, and phase quadrature components, the accuracy and noise robustness of phase estimation are improved.
Article
Chemistry, Analytical
Jinyu Zhang, Taiyang Hu, Xiaolang Shao, Mengxuan Xiao, Yingjiao Rong, Zelong Xiao
Summary: The paper introduces a method of multi-target tracking using windowed Fourier single-pixel imaging (WFSI), which estimates the displacements of independently moving targets through independent and joint estimation, verifying its accuracy and effectiveness.