Relevant bibliographies by topics / 3D-Fourier coefficients

Academic literature on the topic '3D-Fourier coefficients'

Author: Grafiati
Published: 30 May 2022
Last updated: 31 May 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic '3D-Fourier coefficients.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "3D-Fourier coefficients"

1

Lytvyn, Oleg N., and Olesya P. Nechuiviter. "3D Fourier Coefficients on the Class of Differentiable Functions and Spline Interflatation." Journal of Automation and Information Sciences 44, no. 3 (2012): 45–56. http://dx.doi.org/10.1615/jautomatinfscien.v44.i3.40.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Zhang, Jianfeng, and Linong Liu. "Optimum split-step Fourier 3D depth migration: Developments and practical aspects." GEOPHYSICS 72, no. 3 (May 2007): S167—S175. http://dx.doi.org/10.1190/1.2715658.

Full text
Abstract:
We present an efficient scheme for depth extrapolation of wide-angle 3D wavefields in laterally heterogeneous media. The scheme improves the so-called optimum split-step Fourier method by introducing a frequency-independent cascaded operator with spatially varying coefficients. The developments improve the approximation of the optimum split-step Fourier cascaded operator to the exact phase-shift operator of a varying velocity in the presence of strong lateral velocity variations, and they naturally lead to frequency-dependent varying-step depth extrapolations that reduce computational cost significantly. The resulting scheme can be implemented alternatively in spatial and wavenumber domains using fast Fourier transforms (FFTs). The accuracy of the first-order approximate algorithm is similar to that of the second-order optimum split-step Fourier method in modeling wide-angle propagation through strong, laterally varying media. Similar to the optimum split-step Fourier method, the scheme is superior to methods such as the generalized screen and Fourier finite difference. We demonstrate the scheme’s accuracy by comparing it with 3D two-way finite-difference modeling. Comparisons with the 3D prestack Kirchhoff depth migration of a real 3D data set demonstrate the practical application of the proposed method.
APA, Harvard, Vancouver, ISO, and other styles
3

Liu, Linong, and Jianfeng Zhang. "3D wavefield extrapolation with optimum split-step Fourier method." GEOPHYSICS 71, no. 3 (May 2006): T95—T108. http://dx.doi.org/10.1190/1.2197493.

Full text
Abstract:
A one-way propagator is proposed for more accurately modeling wide-angle wavefields in the presence of severe lateral variations of the velocity. The method adds a higher-order correction to improve the split-step Fourier method by directly designing a cascaded operator that matches the exact phase-shift operator of a varying velocity. Using an optimization scheme, the coefficients in the cascaded operator are determined according to the local velocity distribution and the prescribed angular range of wavefield propagation. The proposed algorithm is implemented alternately in spatial and wavenumber domains using fast Fourier transforms, as in the split-step Fourier and generalized-screen methods. This algorithm can achieve higher accuracy than the generalized-screen method for wide-angle wavefields, although the same numerical scheme is used with comparable computational cost. No extra error arises for the proposed algorithm when used for 3D wave propagation, in contrast to methods that introduce an implicit finite–difference higher-order correction to the split-step Fourier method, such as the Fourier finite difference (FFD) and wide-angle screen methods. A detailed comparison of the proposed one-way propagator with the split-step Fourier, generalized-screen, and FFD methods is presented. The 2D Marmousi and 3D SEG/EAEG overthrust data sets are used to test the prestack depth-migration schemes developed based on the proposed one-way propagators.
APA, Harvard, Vancouver, ISO, and other styles
4

Zozulya, V. V. "A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories." Journal of Engineering 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/590480.

Full text
Abstract:
A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.
APA, Harvard, Vancouver, ISO, and other styles
5

Zwartjes, P., and A. Gisolf. "Fourier reconstruction of marine-streamer data in four spatial coordinates." GEOPHYSICS 71, no. 6 (November 2006): V171—V186. http://dx.doi.org/10.1190/1.2348633.

Full text
Abstract:
Many methods exist for interpolation of seismic data in one and two spatial dimensions, but few can interpolate properly in three or four spatial dimensions. Marine multi-streamer data typically are sampled relatively well in the midpoint and absolute offset coordinates but not in the azimuth because the crossline shot coordinate is significantly under sampled. We approach the problem of interpolation of marine-streamer data in four spatial dimensions by splitting the problem into a 1D interpolation along the densely sampled streamers and a 3D Fourier reconstruction for the remaining spatial coordinates. In Fourier reconstruction, the Fourier coefficients that synthesize the nonuniformly sampled seismic data are estimated in a least-squares inversion. The method is computationally efficient, requires no subsurface information, and can handle uniform grids with missing data as well as nonuniform grids or random sampling. The output grid of the 1D interpolation in the first step is arbitrary. When the output grid has uniform inline midpoints spacing, the 3D Fourier reconstruction in the second step is performed in the crossline midpoint, absolute offset, and azimuth coordinates. When the first step outputs to uniform absolute offset, the 3D Fourier reconstruction handles the crossline/inline midpoint and the azimuth coordinates. In both cases, the main innovation is the inclusion of the azimuthal coordinate in the Fourier reconstruction. The azimuth multiplicity must be increased for the method to be successful, which means that overlap shooting is required. We have tested the algorithm on synthetic streamer data for which the proposed method outperforms an approach where the azimuthal coordinate is ignored. Potential applications are interpolation of marine streamer data to decrease the crossline source sampling for the benefit of 3D multiple prediction and regularization to reduce sampling-related differences in processing of time-lapse data.
APA, Harvard, Vancouver, ISO, and other styles
6

Downton, Jonathan E., and Benjamin Roure. "Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters." Interpretation 3, no. 3 (August 1, 2015): ST9—ST27. http://dx.doi.org/10.1190/int-2014-0235.1.

Full text
Abstract:
Amplitude variation with offset and azimuth (AVOAz) analysis can be separated into two separate parts: amplitude variation with offset (AVO) analysis and amplitude variation with azimuth (AVAz) analysis. Useful information about fractures and anisotropy can be obtained just by examining the AVAz. The AVAz can be described as a sum of sinusoids of different periodicities, each characterized by its magnitude and phase. This sum is mathematically equivalent to a Fourier series, and hence the coefficients describing the AVAz response are azimuthal Fourier coefficients (FCs). This FC parameterization is purely descriptive. The aim of this paper is to help the interpreter understand what these coefficients mean in terms of anisotropic and fracture parameters for the case of P-wave reflectivity using a linearized approximation. The FC representation is valid for general anisotropy. However, to gain insight into the significance of FCs, more restrictive assumptions about the anisotropy or facture system must be assumed. In the case of transverse isotropic media with a horizontal axis of symmetry, the P-wave reflectivity linearized approximation may be rewritten in terms of azimuthal FCs with the magnitude and phase of the different FCs corresponding to traditional AVAz attributes. Linear slip theory is used to show that the FCs can be interpreted similarly for the cases of a single set of parallel vertical fractures in isotropic media and in transverse isotropic media with a vertical axis of symmetry (VTI). The magnitude of the FCs depends on the fracture weakness parameters and the background media. For the case of vertical fractures in a VTI background, the AVOAz inverse problem is underdetermined, so extra information must be incorporated to determine how the weights are modified due to this background anisotropy. We evaluated this on a 3D data set from northwest Louisiana for which the main target was the Haynesville shale.
APA, Harvard, Vancouver, ISO, and other styles
7

Guo, Tongqing, Di Zhou, and Zhiliang Lu. "A Double-Passage Shape Correction Method for Predictions of Unsteady Flow and Aeroelasticity in Turbomachinery." Advances in Applied Mathematics and Mechanics 9, no. 4 (January 18, 2017): 839–60. http://dx.doi.org/10.4208/aamm.2016.m1478.

Full text
Abstract:
AbstractIn this paper, a double-passage shape correction (DPSC) method is presented for simulation of unsteady flows around vibrating blades and aeroelastic prediction. Based on the idea of phase-lagged boundary conditions, the shape correction method was proposed aimed at efficiently dealing with unsteady flow problems in turbomachinery. However, the original single-passage shape correction (SPSC) may show the disadvantage of slow convergence of unsteady solutions and even produce nonphysical oscillation. The reason is found to be related with the disturbances on the circumferential boundaries that can not be damped by numerical schemes. To overcome these difficulties, the DPSC method is adopted here, in which the Fourier coefficients are computed from flow variables at implicit boundaries instead of circumferential boundaries in the SPSC method. This treatment actually reduces the interaction between the calculation of Fourier coefficients and the update of flow variables. Therefore a faster convergence speed could be achieved and also the solution stability is improved. The present method is developed to be suitable for viscous and turbulent flows. And for real three-dimensional (3D) problems, the rotating effects are also considered. For validation, a 2D oscillating turbine cascade, a 3D oscillating flat plate cascade and a 3D practical transonic fan rotor are investigated. Comparisons with experimental data or other solutions and relevant discussions are presented in detail. Numerical results show that the solution accuracy of DPSC method is favorable and at least comparable to the SPSC method. However, fewer iteration cycles are needed to get a converged and stable unsteady solution, which greatly improves the computational efficiency.
APA, Harvard, Vancouver, ISO, and other styles
8

Nadeem, Qurrat-Ul-Ain, Abla Kammoun, Merouane Debbah, and Mohamed-Slim Alouini. "A Generalized Spatial Correlation Model for 3D MIMO Channels Based on the Fourier Coefficients of Power Spectrums." IEEE Transactions on Signal Processing 63, no. 14 (July 2015): 3671–86. http://dx.doi.org/10.1109/tsp.2015.2430841.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Tsai, Yu-Chung, and Kuo-Shih Tseng. "Deep Compressed Sensing for Learning Submodular Functions." Sensors 20, no. 9 (May 2, 2020): 2591. http://dx.doi.org/10.3390/s20092591.

Full text
Abstract:
The AI community has been paying attention to submodular functions due to their various applications (e.g., target search and 3D mapping). Learning submodular functions is a challenge since the number of a function’s outcomes of N sets is 2 N . The state-of-the-art approach is based on compressed sensing techniques, which are to learn submodular functions in the Fourier domain and then recover the submodular functions in the spatial domain. However, the number of Fourier bases is relevant to the number of sets’ sensing overlapping. To overcome this issue, this research proposed a submodular deep compressed sensing (SDCS) approach to learning submodular functions. The algorithm consists of learning autoencoder networks and Fourier coefficients. The learned networks can be applied to predict 2 N values of submodular functions. Experiments conducted with this approach demonstrate that the algorithm is more efficient than the benchmark approach.
APA, Harvard, Vancouver, ISO, and other styles
10

Lytvyn, Oleg, Oleg Lytvyn, and Oleksandra Lytvyn. "Analysis of the results of a computational experiment to restore the discontinuous functions of two variables using projections." Physico-mathematical modelling and informational technologies, no. 33 (September 2, 2021): 12–17. http://dx.doi.org/10.15407/fmmit2021.33.012.

Full text
Abstract:
This article presents the main statements of the method of approximation of discontinuous functions of two variables, describing an image of the surface of a 2D body or an image of the internal structure of a 3D body in a certain plane, using projections that come from a computer tomograph. The method is based on the use of discontinuous splines of two variables and finite Fourier sums, in which the Fourier coefficients are found using projection data. The method is based on the following idea: an approximated discontinuous function is replaced by the sum of two functions – a discontinuous spline and a continuous or differentiable function. A method is proposed for constructing a spline function, which has on the indicated lines the same discontinuities of the first kind as the approximated discontinuous function, and a method for finding the Fourier coefficients of the indicated continuous or differentiable function. That is, the difference between the function being approximated and the specified discontinuous spline is a function that can be approximated by finite Fourier sums without the Gibbs phenomenon. In the numerical experiment, it was assumed that the approximated function has discontinuities of the first kind on a given system of circles and ellipses nested into each other. The analysis of the calculation results showed their correspondence to the theoretical statements of the work. The proposed method makes it possible to obtain a given approximation accuracy with a smaller number of projections, that is, with less irradiation.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "3D-Fourier coefficients"

1

Литвин, О. М., О. Г. Литвин, and О. О. Литвин. "Method of Calculating Fourier Coefficients of Three Variable Functions Using Tomogram." Thesis, 2019. http://openarchive.nure.ua/handle/document/9457.

Full text
Abstract:
A method for calculating Fourier coefficients of functions of three variables using tomograms is proposed and investigated. Earlier Lytvyn O.M. proposed and introduced the method of calculating Fourier coefficients of the function of two variables using integrals of this function along a given system of direct. It is believed that these integrals - projections or projection data arrive from a computer tomograph.
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "3D-Fourier coefficients"

1

Nadeem, Qurrat-Ul-Ain, Abla Kammoun, Merouane Debbah, and Mohamed-Slim Alouini. "Spatial correlation in 3D MIMO channels using fourier coefficients of power spectrums." In 2015 IEEE Wireless Communications and Networking Conference (WCNC). IEEE, 2015. http://dx.doi.org/10.1109/wcnc.2015.7127463.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Dong, Qingbing, Jing Wei, Yan Li, and Lixin Xu. "A Numerical Model to Predict Dynamic Performance of Layered Gears at Starved Lubrication." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97276.

Full text
Abstract:
Abstract Gears of modern industry are required to have a good fatigue performance to transmit power and motion through the contact interfaces. Composite layered surfaces can effectively improve the damage resistance of gears and decrease the friction coefficients. However, improper surface modification may induce intensive stress concentrations at the joint interfaces of the strengthening layers and cause unexpected damages to the flanks. Furthermore, the amount of lubricant at the inlet may probably be insufficient to establish fully flooded condition, which may result in starvation and accelerate damages to the gear sets. In this study, a starved elastohydrodynamic lubrication (EHL) model in three-dimensional (3D) line contact for layered gears is developed. The potential energy method is employed to determine the load distribution along the action line. The loading force is assumed to be balanced by the lubrication pressure, which is derived by discretizing the dimensional Reynolds equation into a solvable matrix with the consideration of the enforced boundary conditions due to the inlet oil supply. The transient evolution of lubrication is investigated to evaluate the load-carrying capability of the lubricant film at various starvation conditions. The influence coefficients related to the displacements and stresses of the layered material system are determined with the assistance of the fast Fourier transform (FFT) algorithm, and the effects of the layer properties and the fabrication methods are evaluated. Such analysis may provide insightful information for the optimization of material systems with fabricated layers and engineering design of gears.
APA, Harvard, Vancouver, ISO, and other styles
3

Kumar, Sandeep, Mark G. Turner, Kiran Siddappaji, and Mark Celestina. "Aerodynamic Design System for Non-Axisymmetric Boundary Layer Ingestion Fans." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-77042.

Full text
Abstract:
Non-uniformities at the engine inlet call for novel design techniques to cater to the performance and aeromechanical challenges. The purpose of the fan system is to mitigate the effects of distortion in the flow and to provide thrust to the vehicle. This paper discusses a harmonic based open source design system (NAX) and demonstrates its capabilities for applications in a boundary layer ingesting fan system. First, a primary baseline design was obtained using a typical axisymmetric design approach for the rotor and OGV (Outlet Guide Vanes). This baseline design now serves as the basis for further development, based on user-defined design features. Subsequently, using this baseline design, a circumferentially non-axisymmetric design of the OGV is obtained by means of inducing perturbations in blade leading edge metal angles using Fourier coefficients and phase values. The other parameters that can be varied radially as Bezier curves and tangentially as Fourier modes are: trailing edge metal angle, chord, lean, sweep, curvature and thickness. A smooth spanwise curvature controlled 3D design of OGV is discussed using the open-source geometry generator, T-Blade3. The OGV geometry files along with the detailed documentation are also available for download on the T-Blade3 website and NAX source code on Github website. This design is further optimized to improve the non-axisymmetric geometric distribution against the distorted flow conditions. The design system proposed here helps in exploration of user-specified parametric design space for development of a non-axisymmetric fan stage. Further, since the design system is modular in nature, it can easily be integrated at multiple process levels for other types of turbomachinery design applications.
APA, Harvard, Vancouver, ISO, and other styles
4

Sato, Koma, and Takeshi Honda. "Analysis Method for CFD Results of Centrifugal Blower in Vacuum Cleaner Using Proper Orthogonal Decomposition." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51178.

Full text
Abstract:
2D and steady analysis have been replaced by 3D and unsteady analysis because of dramatic improvements in computational environments. Analysis models that faithfully simulate actual products conventionally tend to be complicated and large scale. Therefore, the storage of analysis results has been increasing tremendously, and the dominant flow-field structure has been difficult to clarify. Data reduction by proper orthogonal decomposition (POD) is effective for simultaneously reducing the number of results of unsteady computational fluid dynamics (CFD) and for comprehending the dominant flow-field structure. However, only a few applications are used in the domain of industrial machinery. In this study, we applied the POD method to unsteady CFD results of a centrifugal blower in a vacuum cleaner and evaluated the benefits. We extracted a time series of static pressure distribution in the diffuser from unsteady CFD results corresponding to one rotation of the impeller, applied the POD to these data, and compared the results of an experiment. The results were that the first six modes had a 99.4% contribution in terms of the L2 norm. In the scope of this research, the first six modes were revealed to surrogate the pressure fluctuation sufficiently. Also, the data storage was reduced to less than 2.0% of the original unsteady results. Next, frequency spectra were obtained by applying a discrete Fourier transform (DFT) to the expansion coefficients. The spectra of the expansion coefficients of the POD modes were found to have a peak near the blade passing frequencies (BPFs). The noise, the frequency of which is BPF, causes the majority of the noise that occurs in the diffuser. Therefore, we found by using both the POD and DFT that we could both reduce the dramatic data storage and extract the flow-field structures.
APA, Harvard, Vancouver, ISO, and other styles
5

Hua, Biaolong, Raphael Lencrerot, Paul Williamson, and Henri Houllevigue. "High-order and high-accuracy 3D Fourier finite difference depth migration with an optimally reduced coefficient table for the tilted transversely isotropic media." In SEG Technical Program Expanded Abstracts 2013. Society of Exploration Geophysicists, 2013. http://dx.doi.org/10.1190/segam2013-1052.1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Matras-Postolek, Katarzyna, A. Zaba, S. Sovinska, and D. Bogdal. "Microwave-assisted preparation of ZnS and ZnSe nanocrystals with different morphologies for photodegradation process of organic dyes." In Ampere 2019. Valencia: Universitat Politècnica de València, 2019. http://dx.doi.org/10.4995/ampere2019.2019.9998.

Full text
Abstract:
Zinc sulphide (ZnS) and zinc selenide (ZnSe) and manganese-doped and un-doped with different morphologies from 1D do 3D microflowers were successfully fabricated in only a few minutes by solvothermal reactions under microwave irradiation. In order to compare the effect of microwave heating on the properties of obtained nanocrystals, additionally the synthesis under conventional heating was conducted additionally in similar conditions. The obtained nanocrystals were systematically characterized in terms of structural and optical properties using X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), diffuse reflectance UV-Vis spectroscopy (DR UV-Vis), Fourier-transform infrared spectroscopy (FT-IR), photoluminescence spectroscopy (PL), X-ray photoelectron spectroscopy (XPS) and Brunauer-Emmett-Teller (BET) surface area analysis. The photocatalytic activity of ZnSe, ZnS, ZnS:Mn and ZnSe:Mn nanocrystals with different morphologies was evaluated by the degradation of methyl orange (MO) and Rhodamine 6G (R6G), respectively. The results show that Mn doped NCs samples had higher coefficient of degradation of organic dyes under ultraviolet irradiation (UV).
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic '3D-Fourier coefficients' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography