The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform
Zhi-chao Zhang - One of the best experts on this subject based on the ideXlab platform.
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Sampling theorem for the short-time linear canonical transform and its applications
Signal Processing, 2015Co-Authors: Zhi-chao ZhangAbstract:In this paper, we propose a sampling theorem for the short-time linear canonical transform (STLCT) by means of a generalized Zak transform associated with the linear canonical transform (LCT). The sampling theorem, which states that the signal can be reconstructed from its sampled STLCT, turns out to be a generalization of the conventional sampling theorem for the short-time Fourier transform (STFT). Based on the new sampling theorem, Gabor's signal expansion in the LCT domain is obtained, which can be considered as a generalization of the classical Gabor expansion and the fractional Gabor expansion, and presents a simpler method for reconstructing the signal from its sampled STLCT. The derived bi-Orthogonality Relation of the generalized Gabor expansion is as simple as that of the classical Gabor expansion, and examples are proposed to verify it. Some potential applications of the linear canonical Gabor spectrum for non-stationary signal processing are also discussed. HighlightsWe propose a new kind of ZT associated with the LCT.We derive the sampling theorem for the STLCT.We obtain Gabor's signal expansion in the LCT domain.The derived bi-Orthogonality Relation is as simple as that of the classical Gabor expansion.We describe some applications of the linear canonical Gabor spectrum.
Baidyanath Patra - One of the best experts on this subject based on the ideXlab platform.
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ON A GENERALISED Orthogonality Relation AND ITS USE IN THE PROBLEM OF ELASTI - CITY OF A TRUNCATED CYLINDRICAL WEDGE.
Journal of the Indian Institute of Science, 2013Co-Authors: Baidyanath PatraAbstract:A generalistd. Orthogonality Relation containing Bessel functions has been derived to use in solving the problem of elasticity in an infinite truncated cylindrical wedge when there are non homogeneous boundary conditions on the lateral sides and homogeneous conditions on the circular surface such that there is symmetry of displacement components about the middle radius.
Won-kwang Park - One of the best experts on this subject based on the ideXlab platform.
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Localization of Small Anomalies via the Orthogonality Sampling Method from Scattering Parameters
Electronics, 2020Co-Authors: Seongje Chae, Chi Young Ahn, Won-kwang ParkAbstract:We investigate the application of the Orthogonality sampling method (OSM) in microwave imaging for a fast localization of small anomalies from measured scattering parameters. For this purpose, we design an indicator function of OSM defined on a Lebesgue space to test the Orthogonality Relation between the Hankel function and the scattering parameters. This is based on an application of the Born approximation and the integral equation formula for scattering parameters in the presence of a small anomaly. We then prove that the indicator function consists of a combination of an infinite series of Bessel functions of integer order, an antenna configuration, and material properties. Simulation results with synthetic data are presented to show the feasibility and limitations of designed OSM.
Sebastian Bielski - One of the best experts on this subject based on the ideXlab platform.
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Comment on the Orthogonality of the Macdonald functions of imaginary order
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Radosław Szmytkowski, Sebastian BielskiAbstract:Abstract Recently, Yakubovich [Opuscula Math. 26 (2006) 161–172] and Passian et al. [J. Math. Anal. Appl. 360 (2009) 380–390] have presented alternative proofs of an Orthogonality Relation obeyed by the Macdonald functions of imaginary order. In this note, we show that the validity of that Relation may be also proven in a simpler way by applying a technique occasionally used in mathematical physics to normalize scattering wave functions to the Dirac delta distribution.
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An Orthogonality Relation for the Whittaker functions of the second kind of imaginary order
Integral Transforms and Special Functions, 2010Co-Authors: Radosław Szmytkowski, Sebastian BielskiAbstract:An Orthogonality Relation for the Whittaker functions of the second kind of imaginary order, W κ, iμ(x), with μ∈ℝ, is investigated. The integral is shown to be proportional to the sum δ(μ−μ′)+δ(μ+μ′), where δ(μ±μ′) is the Dirac delta distribution. The proportionality factor is found to be π2/[μsinh(2πμ) Γ(1/2−κ+iμ) Γ(1/2−κ−iμ)]. For κ=0, the derived formula reduces to the Orthogonality Relation for the Macdonald functions of imaginary order, discussed recently in the literature.
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an Orthogonality Relation for the whittaker functions of the second kind of imaginary order
arXiv: Classical Analysis and ODEs, 2009Co-Authors: Radosław Szmytkowski, Sebastian BielskiAbstract:An Orthogonality Relation for the Whittaker functions of the second kind of imaginary order, $W_{\kappa,\mathrm{i}\mu}(x)$, with $\mu\in\mathbb{R}$, is investigated. The integral $\int_{0}^{\infty}\mathrm{d}x\: x^{-2}W_{\kappa,\mathrm{i}\mu}(x)W_{\kappa,\mathrm{i}\mu'}(x)$ is shown to be proportional to the sum $\delta(\mu-\mu')+\delta(\mu+\mu')$, where $\delta(\mu\pm\mu')$ is the Dirac delta distribution. The proportionality factor is found to be $\pi^{2}/[\mu\sinh(2\pi\mu)\Gamma({1/2}-\kappa+\mathrm{i}\mu) \Gamma({1/2}-\kappa-\mathrm{i}\mu)]$. For $\kappa=0$ the derived formula reduces to the Orthogonality Relation for the Macdonald functions of imaginary order, discussed recently in the literature.
Markus Fritzsche - One of the best experts on this subject based on the ideXlab platform.
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Application of Orthogonality-Relation for the separation of Lamb modes at a plate edge: Numerical and experimental predictions
Ultrasonics, 2015Co-Authors: Madis Ratassepp, Gérard Maze, Aleksander Klauson, Farid Chati, Dominique Decultot, F. León, Markus FritzscheAbstract:In this study the Orthogonality Relation-based method for post-processing finite element (FE) predictions and experimental measurements is applied in order to separate Lamb modes at a plate edge at normal incidence. The scattered wave field from the free edge is assumed to be a superposition of all the eigenmodes of an infinite plate. The eigenmode amplitudes of the reflected wave field are determined by implementing the Orthogonality-based method on the measured plate edge displacements. Overlapping wavepackets of Lamb modes at a plate edge are simulated by using the FE model and the experiment in the case of an incident S0 mode in a plate with a notch. In the experiment a 3D Scanning Laser Doppler Vibrometer (3D SLDV) (Johansmann and Sauer, 2005) is used to measure 3 dimensional vibrations and thus the edge two-dimensional displacement components simultaneously. It is demonstrated that it is possible to extract signals of various propagating and non-propagating modes in time-domain. The influences of the errors in practical measurements on the extraction procedure have also been studied.
