Papers by Keyword: Fourier Transform

Abstract: To perform the Hilbert transform H_il of a non-integrable function φ, such as φ(x) = 1, x, in a numerical calculation-friendly way, we propose a method of rewriting H_il in terms of the resolvent for a differential operator R whose eigenfunctions satisfy the orthogonality and the completeness, so that the resolvent kernel 〈x|R^-1y〉can be given by the eigenfunction expansion. We deal with two cases for the choice of R: one is the harmonic oscillator Hamiltonian, which is commutative with the Fourier transform F; and the other is such that is commutative with H_il itself. We show how the calculation of H_ilφ is made in a numerical calculation-friendly way, to find that Π_k=0,1 H_ilf_k (f_k (x) = x^k) satisfies quite a simple relation.

Abstract: In this paper, we will compare the methods of solving with explicit or implicit finite difference of the partial differential equations that define the mechanical models of hydrodynamics movements, thermodynamics or those that define the vibration movements with the ones that use integral transforms. By applying the Laplace and Fourier transforms, finite in sine or cosine, depending on the boundary conditions of the real physical problem, it leads to the algebraic approach of the problem, which reduces the difficulty of solving partial differential equations. The errors obtained for the solution of partial differential equations using different methods are within the standard norms. However, in terms of calculus precision, the use of integral transforms is more advantageous.

Abstract: In the paper, the array ordering of the TiO₂ nanotubes obtained by method of the anodic oxidation in different modes in the fluorine-containing aqueous-non-aqueous electrolytes containing glycerin as well as the surface-active reagents is considered. It was shown that such characteristics as the two-dimensional Fourier-spectrum, autocorrelation function and its spectrum allow us to identify the ordering nature and to obtain the preliminary quantitative estimates of SEM order.

Abstract: The submitted paper is focused on the design of Tuned Mass Damper in order to reduce excessive level of vibration. This device is designed to be active at the first natural frequency of the structure. Subsequently, the efficiency of the new dynamic system (structure-TMD) is verified for several types of time-dependent loads, which express swaying vandal, jumping vandal and moving pedestrian.

Abstract: Conventional serial and workshop productions use specific parameter ranges to evaluate the quality of a process. Our research showed that parameters within tolerances do not ensure good quality of the final product due to malicious parameter combinations along the assembly line. Therefore, data sets from assembly processes like force-way or force-time curves and quality measurements are evaluated in this novel approach. Using Fourier Transform, k-means, decision trees and a dynamic envelope curve, classification and process monitoring are processed in time and frequency domain. This enables new possibilities to characterize quality and process data, for advanced error detection as well as a more simplified tracing of faults. Here, holistic optimization and monitoring follows two strategies. First, a simplified tracing approach of malicious impacts regards quality results from test benches. Therefore, assembly processes are monitored and characterized by quality data. Second, defective influences, like tool break or calibration errors, are linked to variations of the usual process behavior. Here, the error detection approach focuses on process data from single assembly stations. This approach uses three different methods. First, Fourier Transform extracts additional information from process, energy and quality data. Second, k-means algorithm is used to cluster quality data and extend the data base. Third, a decision tree classifies the quality of the final good and characterizes assembly processes. Last, results of k-means clustering and selected classification methods are compared. This combination allows to increase process quality, improve product quality and reduce failure costs.

Abstract: Spatial-carrier digital speckle pattern interferometry (SC-DSPI) has proven to be a competitive tool for full-field deformation measurement. Comparing with traditional phase-shifting digital speckle pattern interferometry, SC-DSPI has the advantage of rapid measurement which guarantees that dynamic deformations can be precisely measured. In this article, a tri-channel SC-DSPI that measures three-dimensional deformations synchronously is introduced. Measuring algorithm as well as optical arrangement is described in detail. Experiments are carried out to verify the validity and evaluate the performance of the proposed technique.

Abstract: AA6xxx alloys are known to suffer from a phenomenon called roping, which is a ridge and valley pattern appearing after stamping is treated as a fatal surface defect for the automotive skin panels. Although the roping is the important factor to determine the exterior quality, it is commonly evaluated by visual check done by inspecting staff, which is very subjective and difficult to measure quantitatively. In this study, to quantify the roping level in detail and easily, a new calculation method based on Fourier transform and using simple device to measure topography is proposed. As a result of analyses for several different AA6022 alloy sheets, it is found that the strong roping surface has the intensive directional pattern along the rolling direction with a specific wavelength. The roping level can be expressed numerically as the ratio between the amplitude of the rolling directional pattern and the average amplitude of each directional pattern. This value shows good agreement with the roping level determined by human observation. Moreover, it is found that the proposed method can be applied to the surface appearance obtained by digital camera without a 3D profiler.

Abstract: Due to the presence of internal structures, metamaterials, a new class of artificial materials, can be engineered to have various unconventional properties during wave interaction. They can be rationally designed to offer controlled mechanical, acoustic or electromagnetic properties through resonant electromagnetic, acoustic or mechanical structures inside the metamaterial. Due to these properties, metamaterials have been effectively used for cloaking, wave guiding and designing filters in the field of optics, electromagnetics, acoustics and elastodynamics. In this paper, a Fourier transfer based methodology is proposed to determine the attenuation bandwidth of a metamaterial instead of using conventional Bloch’s theorem. The applicability of this method is wider than that of Bloch’s theorem, because this method allows analysis beyond the necessary periodicity of the metamaterial. All the governing equations are non-dimensionalised to effectively quantify the attenuation bandwidth at the lower and higher frequency range of the resonating frequency of the internal structures present in the matrix of the material. The attenuation bandwidth is characterized into low and high frequency parts to determine the effect of the variation of the mass ratio and the number of the repeating units on the attenuation bandwidth of the 1D metamaterial chain.

Abstract: This paper presents the technique of decomposition of form deviation based on the use of wavelet filter and Fourier transform. The method allows decomposing the total deviation into systematic, random systematic (waviness) and random components. The method testing was carried out for the statistics of the deviation of the suction side of the turbine engine compressor blade. The accuracy check of the estimates of form deviations generated by the method in a series of simulated surfaces with pre-laid characteristics was carried out. The results showed that the method of decomposition allows one to estimate exactly the components of the form deviation of the simulated surfaces in their series.

Abstract: Woven fabric texture was periodic and complex, the woven fabric texture analysis method was based on Fourier transform and Gabor transform. Firstly the frequency range of woven fabric texture was obtained by using the Fourier Transform method, and the influence on fabric frequency of image resolution and fabric density was analyzed. Then the main parameters of Gabor filter was confirmed by the woven fabric texture frequency, and the sub-images which contain different texture information were obtained after the woven fabric images were decomposed and fused in different scales and directions using the Gabor filters. Finally the main texture enhancement method, the main texture elimination method, the direntional texture analysis method and extraessential texture enhancement method were discussed. The experiment proved that this method would be a powerful tool in the application of texture analysis.