Search Results (63)

Automatic modulation classification (AMC) is a fundamental technique in wireless communication systems, as it enables the identification of modulation schemes at the receiver without prior knowledge, thereby promoting efficient spectrum utilization. Recent advancements in deep learning (DL) have significantly enhanced classification performance by enabling neural networks (NNs) to learn complex decision boundaries directly from raw signal data. However, many existing NN-based AMC methods employ deep or specialized network architectures, which, while effective, tend to involve substantial structural complexity. To address this issue, we present a simple NN architecture that utilizes features derived from Hankelized matrices to extract informative signal representations. In the proposed approach, received signals are first transformed into Hankelized matrices, from which informative features are extracted using singular value decomposition (SVD). These features are then fed into a compact, fully connected (FC) NN for modulation classification across a wide range of signal-to-noise ratio (SNR) levels. Despite its architectural simplicity, the proposed method achieves competitive performance, offering a practical and scalable solution for AMC tasks at the receiver in diverse wireless environments. Full article

Axially symmetric Taylor–Couette flows of incompressible second grade fluids induced by time-dependent couples inside an infinite circular cylinder are studied under the action of an external magnetic field. The influence of the medium porosity is taken into account in the mathematical modeling. Analytical expressions for the dimensionless non-trivial shear stress and the corresponding fluid velocity were determined using the finite Hankel and Laplace transforms. The solutions obtained are new in the specialized literature and can be customized for various problems of interest in engineering practice. For illustration, the cases of oscillating and constant couples have been considered, and the steady state components of the shear stresses were presented in equivalent forms. Numerical schemes based on finite differences have been formulated for determining the numerical solutions of the proposed problem. It was shown that the numerical results based on analytical solutions and those obtained with the numerical methods have close values with very good accuracy. It was also proved that the fluid flows more slowly and the steady state is reached earlier in the presence of a magnetic field or porous medium. Full article

Conventional synchronization signal detection methods rely on linear correlation function analysis with fixed thresholds, which are insufficient for handling the nonlinear characteristics of practical wireless communication systems. In such environments, the usage of a long synchronization signal is beneficial for ensuring sufficient correlation information and enhancing detection robustness. To address these problems, this paper proposes a novel framework that combines Hankelization-based preprocessing with the operation of a neural network (NN). The proposed method enhances feature extraction through the inverse Fourier transform and Hankel matrix construction, followed by singular value decomposition (SVD) to preserve dominant signal features and suppress noise components. Leveraging the ability of NNs to learn nonlinear patterns, the proposed method eliminates the need for fixed thresholds and achieves robust synchronization signal detection. The simulation results demonstrate superior accuracy in various environments compared to conventional methods, underscoring the potential of Hankelization-based preprocessing in future wireless communication systems. Full article

By leveraging amplitude differences between reflected and diffracted signals in Ground Penetrating Radar (GPR) data, multiple singular spectrum analysis (MSSA) is considered an attractive approach to separate diffraction, which has identified great potential in their detectability of small-scale geological structures. However, conventional MSSA encounters difficulties in pinpointing the singular value threshold that corresponds to reflection, diffraction, and noise within the singular spectrum, leading to a resolution loss of the extracted diffraction profile. To address this issue, this paper develops a new technique that incorporates multilevel wavelet transform (MWT) and MSSA to separate GPR diffraction. By first implementing the MWT on GPR data decompose, the strategy can obtain various approximate detailed coefficients of multiple transformation levels for the subsequent inverse MWT to construct the corresponding coefficient profile. The issue of coefficient profiles that depict reflections often contains residual diffractions is also addressed by performing multiple singular spectrum SVDs based on the Hankel matrix within the dominant frequency domain. Building upon this, the k-means clustering algorithm is introduced to perform MSSA for classifying singular values into k categories. The diffraction wavefield is rebuilt by combining these outcomes with the coefficient profiles that depict diffractions at various transformation levels. Numerical tests showcase that the biorthogonal wavelet basis function bior4.4 provides remarkably efficient GPR diffraction separation performance, and the number of clusters in the k-means clustering algorithm typically ranges from 9 to 15, accounting for the complexity of the wave components. Compared to plane wave deconstruction (PWD), the proposed MWT-MSSA approach reduces energy loss at the diffraction vertex, decreases residual diffraction energy within the reflection profile, and enhances computational efficiency by approximately 70–80% to facilitate the subsequent subtle imaging. Full article

This paper explores the extension of classical transforms to fractal spaces, focusing on the development and application of the Fractal Hankel Transform. We begin with a concise review of fractal calculus to set the theoretical groundwork. The Fractal Hankel Transform is then introduced, along with its formulation and properties. Applications of this transform are presented to demonstrate its utility and effectiveness in solving problems within fractal spaces. Finally, we conclude by summarizing the key findings and discussing potential future research directions in the field of fractal analysis and transformations. Full article

An analytical solution is presented for axisymmetric free vibration analysis of a functionally graded piezoelectric circular plate on the basis of the three-dimensional elastic theory of piezoelectric materials. The material properties are assumed to follow an exponential law distribution through the thickness of the circular plate. The state space equations for the free vibration behavior of the functionally graded piezoelectric circular plate are developed based on the state space method. The finite Hankel transform is utilized to obtain an ordinary differential equation with variable coefficients. By virtue of the proposed exponential law model, we have ordinary differential equations with constant coefficients. Then, the free vibration behaviors of the functionally graded piezoelectric circular plate with two kinds of boundary conditions are investigated. Some numerical examples are given to validate the accuracy and stability of the present model. The influences of the exponential factor and thickness-to-span ratio on the natural frequency of the functionally graded piezoelectric circular plate, constrained by different boundary conditions, are discussed in detail. Full article

The presented article is about the axisymmetric deformation of an annular one-dimensional hexagonal piezoelectric quasicrystal actuator/sensor with different configurations, analyzed by the three-dimensional theory of piezoelectricity coupled with phonon and phason fields. The state space method is utilized to recast the basic equations of one-dimensional hexagonal piezoelectric quasicrystals into the transfer matrix form, and the state space equations of a laminated annular piezoelectric quasicrystal actuator/sensor are obtained. By virtue of the finite Hankel transform, the ordinary differential equations with constant coefficients for an annular quasicrystal actuator/sensor with a generalized elastic simple support boundary condition are derived. Subsequently, the propagator matrix method and inverse Hankel transform are used together to achieve the exact axisymmetric solution for the annular one-dimensional hexagonal piezoelectric quasicrystal actuator/sensor. Numerical illustrations are presented to investigate the influences of the thickness-to-span ratio on a single-layer annular piezoelectric quasicrystal actuator/sensor subjected to different top surface loads, and the effect of material parameters is also presented. Afterward, the present model is applied to compare the performance of different piezoelectric quasicrystal actuator/sensor configurations: the quasicrystal multilayer, quasicrystal unimorph, and quasicrystal bimorph. Full article

In this study, the $k$-Oresme and $k$-Oresme-Lucas sequences are defined, and some terms of these sequence are given. Then, the relations between the terms of the $k$-Oresme and $k$-Oresme-Lucas sequences are presented. In addition, we give these sequences the Binet formulas, generating functions, Cassini identity, Catalan identity etc. Moreover, the $k$-Oresme and $k$-Oresme-Lucas sequences are associated with Fibonacci, Pell numbers and Lucas, and Pell- Lucas numbers, respectively. Finally, the Catalan transforms of these sequences are given and Hankel transforms are applied to these Catalan sequences and associated with the terms of the sequence. Full article

To achieve high-precision calculation of the electromagnetic field of layered media and to ensure that the apparent resistivity calculation and sensitivity are not affected by numerical errors, this paper implements high-precision calculation of the layered electromagnetic field based on the weighted average (WA) extrapolation method. Firstly, the 1D electromagnetic field expression of an arbitrary attitude field source is obtained by using the magnetic vector potential; then, the WA extrapolation technique is introduced to achieve the high-precision and fast solution of the Hankel transform, and the effects of the number of Gaussian points and the number of integration intervals on the accuracy are investigated. The theoretical model test shows that, compared with the open-source Dipole1D, the algorithm proposed in this paper has wider adaptability, and can achieve high-precision calculation of electric and magnetic dipole sources with higher efficiency. Compared with the epsilon algorithm studied by previous researchers, the WA extrapolation method proposed in this article can improve the convergence rate by approximately 20% under the same conditions. It can obtain high-precision numerical solutions with less integration time. The relative accuracy can reach the order ${10}^{-10}$, and its computational efficiency is significantly better than the existing epsilon algorithm. Finally, we used two cases of marine controlled source electromagnetic method to show the application. The sensitivity and Poynting vectors are calculated, which provides a technical tool for a deep understanding of physical mechanisms in layered media. Full article

The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and optics. This paper investigates two sampling theorems for interpolating bandlimited and highest frequency bandlimited functions in the OLCT and offset linear canonical Hankel transform (OLCHT) domains by polar coordinates. Based on the classical Stark’s interpolation formulas, we derive the sampling theorems for bandlimited functions in the OLCT and OLCHT domains, respectively. The first interpolation formula is concise and applicable. Due to the consistency of the OLCHT order, the second interpolation formula is superior to the first interpolation formula in computational complexity. Full article

In singular spectrum analysis, which is applied to signal extraction, it is of critical importance to select the number of components correctly in order to accurately estimate the signal. In the case of a low-rank signal, there is a challenge in estimating the signal rank, which is equivalent to selecting the model order. Information criteria are commonly employed to address these issues. However, singular spectrum analysis is not aimed at the exact low-rank approximation of the signal. This makes it an adaptive, fast, and flexible approach. Conventional information criteria are not directly applicable in this context. The paper examines both subspace-based and information criteria, proposing modifications suited to the Hankel structure of trajectory matrices employed in singular spectrum analysis. These modifications are initially developed for white noise, and a version for red noise is also proposed. In the numerical comparisons, a number of scenarios are considered, including the case of signals that are approximated by low-rank signals. This is the most similar to the case of real-world time series. The criteria are compared with each other and with the optimal rank choice that minimizes the signal estimation error. The results of numerical experiments demonstrate that for low-rank signals and noise levels within a region of stable rank detection, the proposed modifications yield accurate estimates of the optimal rank for both white and red noise cases. The method that considers the Hankel structure of the trajectory matrices appears to be a superior approach in many instances. Reasonable model orders are obtained for real-world time series. It is recommended that a transformation be applied to stabilize the variance before estimating the rank. Full article

We present a novel proof, using group theory, for a Meijer transform formula. This proof reveals the formula as a specific case of a broader generalized result. The generalization is achieved through a linear operator that intertwines two representations of the connected component of the identity of the group $\mathrm{SO}(2,2)$. Using this same approach, we derive a formula for the sum of three double integral transforms, where the kernels are represented by Bessel functions. It is particularly noteworthy that the group $\mathrm{SO}(2,2)$ is connected to symmetry in several significant ways, especially in mathematical physics and geometry. Full article

The aim of this paper is to define the linear operator based on the generalized Mittag-Leffler function and the Lambert series. By using this operator, we introduce a new subclass of β-uniformly starlike functions ${\mathsf{{\rm T}}}_{\mathcal{J}}\left({\alpha }_i\right)$. Further, we obtain coefficient estimates, convex linear combinations, and radii of close-to-convexity, starlikeness, and convexity for functions ${f\in \mathsf{{\rm T}}}_{\mathcal{J}}\left({\alpha }_i\right)$. In addition, we investigate the inclusion conditions of the Hadamard product and the integral transform. Finally, we determine the second Hankel inequality for functions belonging to this subclass. Full article

This article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating function under the integral can be fulfilled either by an exponential or by its product by the Hankel function. The proposed types of Sommerfeld integrals are generalized on the basis of integral representations of the Hertz radiator fields in the form of the inverse Hankel transform with the subsequent replacement of the Bessel function by the Hankel function. It is shown that the numerical values of the saddle point are complex. During integration, reference or so-called standard integrals, which contain the main features of the integrand function, were used. As a demonstration of the accuracy of the technique, a previously known asymptotic formula for the Hankel functions was obtained in the form of an infinite series. The proposed method for calculating Sommerfeld integrals can be useful in solving the half-space Sommerfeld problem. The authors present an example in the form of an infinite series for the magnetic field of reflected waves, obtained directly through the Sommerfeld integral (SI). Full article

Array sensor failure poses a serious challenge to robust direction-of-arrival (DOA) estimation in complicated environments. Although existing matrix completion methods can successfully recover the damaged signals of an impaired sensor array, they cannot preserve the multi-way signal characteristics as the dimension of arrays expands. In this paper, we propose a structural-missing tensor completion algorithm for robust DOA estimation with uniform rectangular array (URA), which exhibits a high robustness to non-ideal sensor failure conditions. Specifically, the signals received at the impaired URA are represented as a three-dimensional incomplete tensor, which contains whole fibers or slices of missing elements. Due to this structural-missing pattern, the conventional low-rank tensor completion becomes ineffective. To resolve this issue, a spatio-temporal dimension augmentation method is developed to transform the structural-missing tensor signal into a six-dimensional Hankel tensor with dispersed missing elements. The augmented Hankel tensor can then be completed with a low-rank regularization by solving a Hankel tensor nuclear norm minimization problem. As such, the inverse Hankelization on the completed Hankel tensor recovers the tensor signal of an unimpaired URA. Accordingly, a completed covariance tensor can be derived and decomposed for robust DOA estimation. Simulation results verify the effectiveness of the proposed algorithm. Full article