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The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the qFT is the mismatch between the spatial and frequency…
In this work, we describe examples for calculating the 1-D circular convolution of signals represented by 3-qubit superpositions. The case is considered, when the discrete Fourier transform of one of the signals is known and calculated in…
We present one- and two-photon diffraction and interference experiments involving parametric down-converted photon pairs. By controlling the divergence of the pump beam in parametric down-conversion, the diffraction-interference pattern…
This tutorial is designed to clarify a few misconceptions in the field of ultrafast optics. (1) Analytic signal that underlies the complex-conjugate decomposition of the field is discussed, as well as the misunderstanding between…
All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier…
It is shown that a classical optical Fourier processor can be used for the shaping of quantum correlations between two or more photons, and the class of Fourier masks applicable in the multiphoton Fourier space is identified. This concept…
Classification of EEG signals using shallow Convolutional Neural Networks (CNNs) is a prevalent and successful approach across a variety of fields. Most of these models use independent one-dimensional (1D) convolutional layers along the…
Fast methods for convolution and correlation underlie a variety of applications in computer vision and graphics, including efficient filtering, analysis, and simulation. However, standard convolution and correlation are inherently limited…
The development of Information and Communication Technologies suggests some spectacular changes in the methods used for teaching scientific subjects. Nowadays, the development of software and hardware makes it possible to simulate processes…
In biomedical imaging analysis, the dichotomy between 2D and 3D data presents a significant challenge. While 3D volumes offer superior real-world applicability, they are less available for each modality and not easy to train in large scale,…
We design a two-dimensional signal constellation based on the exact periodic inverse nonlinear Fourier transform. Feasibility of continuous transmission with periodic signals is experimentally demonstrated over more than 2000 km.
Previous research has shown that computation of convolution in the frequency domain provides a significant speedup versus traditional convolution network implementations. However, this performance increase comes at the expense of repeatedly…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
Continuum soft robots, composed of flexible materials, exhibit theoretically infinite degrees of freedom, enabling notable adaptability in unstructured environments. Cosserat Rod Theory has emerged as a prominent framework for modeling…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
Conventional optical synthesis, the manipulation of the phase and amplitude of spectral components to produce an optical pulse in different temporal modes, is revolutionizing ultrafast optical science and metrology. These technologies rely…
All organisms make temporal predictions, and their evolutionary fitness level depends on the accuracy of these predictions. In the context of visual perception, the motions of both the observer and objects in the scene structure the…
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images.…
Convolutional neural network (CNN) is one of the most widely-used successful architectures in the era of deep learning. However, the high-computational cost of CNN still hampers more universal uses to light devices. Fortunately, the Fourier…