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Wyniki wyszukiwania dla: discrete radon transform
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Discrete convolution based on polynomial residue representation
PublikacjaThis paper presents the study of fast discrete convolution calculation with use of the Polynomial Residue Number System (PRNS). Convolution can be based the algorithm similar to polynomial multiplication. The residue arithmetic allows for fast realization of multiplication and addition, which are the most important arithmetic operations in the implementation of convolution. The practical aspects of hardware realization of PRNS...
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Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform
PublikacjaBirth–and–death models are now a common mathematical tool to describe branching patterns observed in real–world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth–and–death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublikacjaIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Discrete Modelling of Micro-structural Phenomena in Granular Shear Zones
PublikacjaThe micro-structure evolution in shear zones in cohesionless sand for quasi-static problems was analyzed with a discrete element method (DEM). The passive sand failure for a very rought retaining wall undergoing horizontal translation towards the sand backfill was discussed. To simulate the behaviour of sand, the spherical discrete element model was used with elements in the form of rigid spheres with contacts moments.
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublikacjaIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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The Farrow structure for the Hilbert transform filter
PublikacjaPrzedstawiono nową implementację cyfrowego filtru Hilberta, wykonaną w strukturze Farrowa. Jest to filtr zespolony, realizujący jednocześnie dwie różne operacje liniowe, wykonywane dotychczas za pomocą osobnych filtrów. Pierwsza z nich polega na standardowej filtracji hilbertowskiej. Tworzy ona zespolony "analityczny" odpowiednik rzeczywistego sygnału wejściowego. Drugą, osiąganą za pomocą prze-próbkowania ze współczynnikiem, w...
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Evaluation of Hilbert transform filter performance
PublikacjaW pracy rozpatrzono zagadnienie adaptacyjnej estymacji ułamkowego opóźnienia pomiędzy dwoma sygnałami sinusoidalnymi. Zastosowano tu nowy, zagregowany, zespolony filtr Hilberta, który łączy w sobie funkcje filtracji Hilberta i kompensacji ułamkowego opóźnienia. W eksperymentach wykorzystano efektywną implementację tego filtru w strukturze Farrowa, której jedynym parametrem o zmiennej wartości jest bieżące opóźnienie ułamkowe.
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Windowing of the Discrete Green's Function for Accurate FDTD Computations
PublikacjaThe paper presents systematic evaluation of the applicability of parametric and nonparametric window functions for truncation of the discrete Green's function (DGF). This function is directly derived from the FDTD update equations, thus the FDTD method and its integral discrete formulation can be perfectly coupled using DGF. Unfortunately, the DGF computations require processor time, hence DGF has to be truncated with appropriate...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublikacjaIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublikacjaIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Investigations of the Methods of Time Delay Measurement of Stochastic Signals Using Cross-correlation with the Hilbert Transform
PublikacjaThe article presents the results of simulation studies of four methods of estimating time delay for random signals using cross-correlation with the Hilbert Transform. Selected models of mutually delayed stochastic signals were used in the simulations, corresponding to the signals obtained from scintillation detectors in radioisotope measurements of liquid-gas two-phase flow. Standard deviations of the values of the individual functions...
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Periodic Properties of 1D FE Discrete Models in High Frequency Dynamics
PublikacjaFinite element discrete models of various engineering 1D structures may be considered as structures of certain periodic characteristics. The source of this periodicity comes from the discontinuity of stress/strain field between the elements. This behaviour remains unnoticeable, when low frequency dynamics of these structures is investigated. At high frequency regimes, however, its influence may be strong enough to dominate calculated...
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Connection matrix theory for discrete dynamical systems
PublikacjaIn [C] and [F1] the connection matrix theory for Morse decomposition is developedin the case of continuous dynamical systems. Our purpose is to study the case of discrete timedynamical systems.
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Fourier-transform infrared spectroscopy (FTIR) spectra of bulk boron and borophene flakes
Dane BadawczeThese data contain Fourier-transform infrared spectroscopy (FTIR) spectra of bulk boron and borophene flakes obtained during ball milling (450 rpm, 6 h, 1 g). Spectra were acquired to investigate the chemical bonds and functional groups on the surface of the pristine boron and borophene flakes.
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Hybridization of the FDTD method with use of the discrete Green's function
PublikacjaIn this contribution, a hybrid technique is presented which combines the finite-difference time-domain (FDTD) method and the discrete Green's function (DGF) formulation of this method. FDTD is a powerful technique for the analysis of complex penetrable objects but its application is not efficient when the computational domain includes many free-space cells. Therefore, the hybrid method was developed which is applicable to complex...
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Index filtrations and Morse decomposition for discrete dynamical systems
PublikacjaOn a Morse decomposition of an isolated invariant set of a homeomorphism(discrete dynamical system) there are partial orderings defined by the homeomorphism.These are called admissible orderings of the...
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Discrete Optimization
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Discrete Analysis
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Non-Destructive Diagnostics of Concrete Beams Strengthened with Steel Plates Using Modal Analysis and Wavelet Transform
PublikacjaExternally bonded reinforcements are commonly and widely used in civil engineering objects made of concrete to increase the structure load capacity or to minimize the negative effects of long-term operation and possible defects. The quality of adhesive bonding between a strengthened structure and steel or composite elements is essential for effective reinforcement; therefore, there is a need for non-destructive diagnostics of adhesive...
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Application of wavelet transform in analysis of guided wave propagation signals for damage detection in a steel plate
PublikacjaThe paper presents results of experimental investigations on damage detection using guided wave propagation technique. The tested specimen was a steel plate with a defect in the form of a rectangular notch. Lamb waves were excited by a PZT actuator and sensed by a laser vibrometer. Since reflections from damage in registered signals are often masked by measurement noise, for identification of time of reflections from damage, continuous...