相关论文: Uncertainty Principles for the Offset Linear Canon…
In this paper, we introduce quaternion offset linear canonical transform of integrable and square integrable functions. Moreover, we show that the proposed transform satisfies all the respective properties like inversion formula, linearity,…
The paper is devoted to the development of the octonion Fourier transform (OFT) theory initiated in 2011 in articles by Hahn and Snopek. It is also a continuation and generalization of earlier work by Blaszczyk and Snopek, where they proved…
The metaplectic transform (MT), a generalization of the Fourier transform sometimes called the linear canonical transform, is a tool used ubiquitously in modern optics, for example, when calculating the transformations of light beams in…
In this paper, we introduce the notion of windowed linear canonical transform in biquaternion setting namely Biquaternion Windowed Linear Canonical Transform (BiQWLCT) and various properties of BiQWLCT, such as linearity, shift, parity,…
In the field of applied mathematics the Fourier transform has developed into an important tool. It is a powerful method for solving partial differential equations. The Fourier transform provides also a technique for signal analysis where…
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
The polar wavelet transform (PWT) has been proven to be a powerful mathematical tool for signal and image processing in recent years. Due to the increasing demand for directional representations of signals in engineering, it is impossible…
The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier…
We define a novel time-frequency analyzing tool, namely linear canonical wavelet transform (LCWT) and study some of its important properties like inner product relation, reconstruction formula and also characterize its range. We obtain…
In this paper, the generic uncertainty relation (UR) for kernel-based transformations (KT) of signals is derived. Instead of using the statistics approach as shown in the literature before, here we employ quantum mechanical operator…
The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and…
We develop a method for the transfer of an uncertainty principle for the short-time Fourier transform or a Fourier pair to an uncertainty principle for a sesquilinear or quadratic metaplectic time-frequency representation. In particular, we…
The Continuous Boostlet Transform (CBT) is introduced as a powerful tool for analyzing spatiotemporal signals, particularly acoustic wavefields. Overcoming the limitations of classical wavelets, the CBT leverages the Poincar\'e group and…
In nature, signals often appear in the form of the superposition of multiple non-stationary signals. The overlap of signal components in the time-frequency domain poses a significant challenge for signal analysis. One approach to addressing…
High-numerical-aperture optical coherence tomography (OCT) enables sub-cellular imaging but faces a trade-off between lateral resolution and depth of focus. Computational refocusing can correct defocus in Fourier-domain OCT, yet its…
Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest…
Optical-model potentials (OMPs) continue to play a key role in nuclear reaction calculations. However, the uncertainty of phenomenological OMPs in widespread use -- inherent to any parametric model trained on data -- has not been fully…
Optical Coherence Tomography (OCT) has become an indispensable tool for investigating mesoscopic features in soft matter and fluid mechanics. Its ability to provide high-resolution, non-invasive measurements in both spatial and temporal…
The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation…
Optical neural networks present distinct advantages over traditional electrical counterparts, such as accelerated data processing and reduced energy consumption. While coherent light is conventionally employed in optical neural networks,…