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Journal articles on the topic 'Spherical harmonic synthesis and analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Xiao, Huadong, and Yang Lu. "Parallel computation for spherical harmonic synthesis and analysis." Computers & Geosciences 33, no. 3 (2007): 311–17. http://dx.doi.org/10.1016/j.cageo.2006.07.005.

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2

Blais, J. A. R., and D. A. Provins. "Spherical harmonic analysis and synthesis for global multiresolution applications." Journal of Geodesy 76, no. 1 (2002): 29–35. http://dx.doi.org/10.1007/s001900100217.

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3

Blais, J. "Discrete Spherical Harmonic Transforms of Nearly Equidistributed Global Data." Journal of Geodetic Science 1, no. 3 (2011): 251–58. http://dx.doi.org/10.2478/v10156-011-0003-1.

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Discrete Spherical Harmonic Transforms of Nearly Equidistributed Global DataDiscrete Spherical Harmonic Transforms (SHTs) are commonly defined for equiangular grids on the sphere. However, when global array data exhibit near equidistributed patterns rather than equiangular grids, discrete SHTs require appropriate adaptations for analysis and synthesis. Computational efficiency and reliability impose structural constraints on possible equidistribution characteristics of data patterns such as for instance with Chebychev quadratures and Fast Fourier Transforms (FFTs). Following some general intro

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4

Hwang, Cheinway, and Yu-Chi Kao. "Spherical harmonic analysis and synthesis using FFT: Application to temporal gravity variation." Computers & Geosciences 32, no. 4 (2006): 442–51. http://dx.doi.org/10.1016/j.cageo.2005.07.006.

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5

Wittwer, Tobias, Roland Klees, Kurt Seitz, and Bernhard Heck. "Ultra-high degree spherical harmonic analysis and synthesis using extended-range arithmetic." Journal of Geodesy 82, no. 4-5 (2007): 223–29. http://dx.doi.org/10.1007/s00190-007-0172-y.

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6

Blais, J. "Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral Data." Journal of Geodetic Science 1, no. 1 (2011): 9–16. http://dx.doi.org/10.2478/v10156-010-0002-7.

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Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral DataSpherical Harmonic Transforms (SHTs) which are non-commutative Fourier transforms on the sphere are critical in global geopotential and related applications. Among the best known global strategies for discrete SHTs of band-limited spherical functions are Chebychev quadratures and least squares for equiangular grids. With proper numerical preconditioning, independent of latitude, reliable analysis and synthesis results for degrees and orders over 3800 in double precision arithmetic have been achieved and ex

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7

Tenzer, Robert, Peter Vajda, and Peter Hamayun. "A mathematical model of the bathymetry-generated external gravitational field." Contributions to Geophysics and Geodesy 40, no. 1 (2010): 31–44. http://dx.doi.org/10.2478/v10126-010-0002-8.

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A mathematical model of the bathymetry-generated external gravitational field The currently available global geopotential models and the global elevation and bathymetry data allow modelling the topography-corrected and bathymetry stripped reference gravity field to a very high spectral resolution (up to degree 2160 of spherical harmonics) using methods for a spherical harmonic analysis and synthesis of the gravity field. When modelling the topography-corrected and crust-density-contrast stripped reference gravity field, additional stripping corrections are applied due to the ice, sediment and

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8

Chen, Wenjin, and Robert Tenzer. "Reformulation of Parker–Oldenburg's method for Earth's spherical approximation." Geophysical Journal International 222, no. 2 (2020): 1046–73. http://dx.doi.org/10.1093/gji/ggaa200.

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SUMMARY Parker–Oldenburg's method is perhaps the most commonly used technique to estimate the depth of density interface from gravity data. To account for large density variations reported, for instance, at the Moho interface, between the ocean seawater density and marine sediments, or between sediments and the underlying bedrock, some authors extended this method for variable density models. Parker–Oldenburg's method is suitable for local studies, given that a functional relationship between gravity data and interface geometry is derived for Earth's planar approximation. The application of th

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9

D'Agostino, Luca, and Christopher E. Brennen. "Linearized dynamics of spherical bubble clouds." Journal of Fluid Mechanics 199 (February 1989): 155–76. http://dx.doi.org/10.1017/s0022112089000339.

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The present work investigates the dynamics of the one-dimensional, unsteady flow of a spherical bubble cloud subject to harmonic far-field pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility and relative motion of the two phases are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. The results are then generalized by means of Fourier synthesis to the case of arbitrary far-field pressure excitation. The flow displays various regimes (sub-reson

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10

Tenzer, Robert. "Inverse problem for the gravimetric modeling of the crust-mantle density contrast." Contributions to Geophysics and Geodesy 43, no. 2 (2013): 83–98. http://dx.doi.org/10.2478/congeo-2013-0006.

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Abstract The gravimetric inverse problem for finding the Moho density contrast is formulated in this study. The solution requires that the crust density structure and the Moho depths are a priori known, for instance, from results of seismic studies. The relation between the isostatic gravity data (i.e., the complete-crust stripped isostatic gravity disturbances) and the Moho density contrast is defined by means of the Fredholm integral equation of the first kind. The closed analytical solution of the integral equation is given. Alternative expressions for solving the inverse problem of isostas

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11

Tenzer, Robert. "Mathematical models of the Earth’s density structure and their applications in gravimetric forward modeling." Contributions to Geophysics and Geodesy 45, no. 2 (2015): 67–92. http://dx.doi.org/10.1515/congeo-2015-0014.

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Abstract A generalized mathematical model of the Earth’s density structure is presented in this study. This model is defined based on applying the spectral expressions for a 3-D density distribution within the arbitrary volumetric mass layers. The 3-D density model is then converted into a form which describes the Earth’s density structure by means of the density-contrast interfaces between the volumetric mass layers while additional correction terms are applied to account for radial density changes. The applied numerical schemes utilize methods for a spherical harmonic analysis and synthesis

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12

Haines, G. V. "Spherical cap harmonic analysis." Journal of Geophysical Research 90, B3 (1985): 2583. http://dx.doi.org/10.1029/jb090ib03p02583.

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13

Mochizuki, E. "Spherical harmonic analysis on hemisphere." Solar Physics 142, no. 2 (1992): 395–98. http://dx.doi.org/10.1007/bf00151462.

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14

MacGillivray, John, and Victor Sparrow. "Greens function modified spherical harmonic analysis." Journal of the Acoustical Society of America 108, no. 5 (2000): 2593. http://dx.doi.org/10.1121/1.4743644.

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15

Bordovský, Jaromír, and Z. Nádeník. "Spherical harmonic analysis and Fourier transformation." Studia Geophysica et Geodaetica 30, no. 1 (1986): 13–27. http://dx.doi.org/10.1007/bf01630849.

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16

Santis, A. "Translated origin spherical cap harmonic analysis." Geophysical Journal International 106, no. 1 (1991): 253–63. http://dx.doi.org/10.1111/j.1365-246x.1991.tb04615.x.

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17

Jekeli, Christopher. "Spherical harmonic analysis, aliasing, and filtering." Journal of Geodesy 70, no. 4 (1996): 214–23. http://dx.doi.org/10.1007/bf00873702.

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18

Krötz, Bernhard, and Henrik Schlichtkrull. "Harmonic Analysis for Real Spherical Spaces." Acta Mathematica Sinica, English Series 34, no. 3 (2017): 341–70. http://dx.doi.org/10.1007/s10114-017-6557-9.

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19

Jekeli, C. "Spherical harmonic analysis, aliasing, and filtering." Journal of Geodesy 70, no. 4 (1996): 214–23. http://dx.doi.org/10.1007/s001900050010.

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20

Parkinson, James. "Spherical harmonic analysis on affine buildings." Mathematische Zeitschrift 253, no. 3 (2006): 571–606. http://dx.doi.org/10.1007/s00209-005-0924-4.

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21

Magyar, A., E. M. Stein, and S. Wainger. "Discrete Analogues in Harmonic Analysis: Spherical Averages." Annals of Mathematics 155, no. 1 (2002): 189. http://dx.doi.org/10.2307/3062154.

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22

Elko, Gary W., and Jens Meyer. "Spherical harmonic beamforming for room acoustic analysis." Journal of the Acoustical Society of America 125, no. 4 (2009): 2544. http://dx.doi.org/10.1121/1.4783614.

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23

Heavens, A. F., and A. N. Taylor. "A spherical harmonic analysis of redshift space." Monthly Notices of the Royal Astronomical Society 275, no. 2 (1995): 483–97. http://dx.doi.org/10.1093/mnras/275.2.483.

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24

Hathaway, David H. "Spherical harmonic analysis of steady photospheric flows." Solar Physics 108, no. 1 (1987): 1–20. http://dx.doi.org/10.1007/bf00152073.

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25

Dezhong, Yao. "Imaging of EEG by spherical harmonic analysis." Journal of Electronics (China) 13, no. 1 (1996): 82–88. http://dx.doi.org/10.1007/bf02684719.

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26

Bannai, Eiichi, Takayuki Okuda, and Makoto Tagami. "Spherical designs of harmonic index t." Journal of Approximation Theory 195 (July 2015): 1–18. http://dx.doi.org/10.1016/j.jat.2014.06.010.

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27

Claessens, S. J. "Spherical harmonic analysis of a harmonic function given on a spheroid." Geophysical Journal International 206, no. 1 (2016): 142–51. http://dx.doi.org/10.1093/gji/ggw126.

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28

Benyamini, Y., and Yitzhak Weit. "Harmonic analysis of spherical functions on $SU(1,1)$." Annales de l’institut Fourier 42, no. 3 (1992): 671–94. http://dx.doi.org/10.5802/aif.1305.

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29

Hathaway, David H. "Spherical harmonic analysis of steady photospheric flows, II." Solar Physics 137, no. 1 (1992): 15–32. http://dx.doi.org/10.1007/bf00146573.

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30

Mochizuki, E. "Spherical harmonic analysis in terms of line integral." Physics of the Earth and Planetary Interiors 76, no. 1-2 (1993): 97–101. http://dx.doi.org/10.1016/0031-9201(93)90057-g.

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31

Bian, S., and J. Menz. "Using piecewise linear interpolations in spherical harmonic analysis." Journal of Geodesy 72, no. 7-8 (1998): 473–81. http://dx.doi.org/10.1007/s001900050186.

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32

Hamza, V. M., R. R. Cardoso, and C. F. Ponte Neto. "Spherical harmonic analysis of earth’s conductive heat flow." International Journal of Earth Sciences 97, no. 2 (2007): 205–26. http://dx.doi.org/10.1007/s00531-007-0254-3.

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33

ITOIGAWA, Fumihiro, Takashi NAKAMURA, and Koichi FUNABASHI. "Harmonic Analysis by Spherical Function for Evaluating Form Error of Spherical Parts." JSME international journal. Ser. 3, Vibration, control engineering, engineering for industry 35, no. 1 (1992): 174–79. http://dx.doi.org/10.1299/jsmec1988.35.174.

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34

ITOIGAWA, Fumihiro, Takashi NAKAMURA, and Koichi FUNABASHI. "Harmonic analysis by spherical function for evaluating form error of spherical parts." Transactions of the Japan Society of Mechanical Engineers Series C 57, no. 533 (1991): 296–301. http://dx.doi.org/10.1299/kikaic.57.296.

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35

Jammalamadaka, S. Rao, and György H. Terdik. "Harmonic analysis and distribution-free inference for spherical distributions." Journal of Multivariate Analysis 171 (May 2019): 436–51. http://dx.doi.org/10.1016/j.jmva.2019.01.012.

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36

Zhao, B. D., D. H. Wei, and J. F. Wang. "Particle shape quantification using rotation-invariant spherical harmonic analysis." Géotechnique Letters 7, no. 2 (2017): 190–96. http://dx.doi.org/10.1680/jgele.17.00011.

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37

Singh, Saransh, Donald E. Boyce, Joel V. Bernier, and Nathan R. Barton. "Discrete spherical harmonic functions for texture representation and analysis." Journal of Applied Crystallography 53, no. 5 (2020): 1299–309. http://dx.doi.org/10.1107/s1600576720011097.

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A basis of discrete harmonic functions for efficient representation and analysis of crystallographic texture is presented. Discrete harmonics are a numerical representation of the harmonics on the sphere. A finite element formulation is utilized to calculate these orthonormal basis functions, which provides several advantageous features for quantitative texture analysis. These include high-precision numerical integration, a simple implementation of the non-negativity constraint and computational efficiency. Simple examples of pole figure and texture interpolation and of Fourier filtering using

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38

Lowes, F. J. "Vector Errors in Spherical Harmonic Analysis of Scalar Data." Geophysical Journal of the Royal Astronomical Society 42, no. 2 (2007): 637–51. http://dx.doi.org/10.1111/j.1365-246x.1975.tb05884.x.

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39

Kharshiladze, A. F., and K. G. Ivanov. "Sector spherical harmonic analysis of the solar magnetic field." Geomagnetism and Aeronomy 53, no. 1 (2013): 1–4. http://dx.doi.org/10.1134/s0016793213010106.

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40

Shankar, S., and K. F. Jensen. "Analysis of spherical harmonic expansion approximations for glow discharges." IEEE Transactions on Plasma Science 23, no. 4 (1995): 780–87. http://dx.doi.org/10.1109/27.468000.

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41

Ertürk, S., and T. J. Dennis. "Fast spherical harmonic analysis (FSHA) for 3D model representation." Electronics Letters 33, no. 18 (1997): 1541. http://dx.doi.org/10.1049/el:19971018.

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42

Gorfinkel’, N. E. "Harmonic analysis on a class of spherical homogeneous spaces." Mathematical Notes 90, no. 5-6 (2011): 678–85. http://dx.doi.org/10.1134/s000143461111006x.

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43

Cartwright, Donald I. "Spherical Harmonic Analysis on Buildings of Type Ã n." Monatshefte f�r Mathematik 133, no. 2 (2001): 93–109. http://dx.doi.org/10.1007/s006050170025.

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44

Avdeev, R. S., and N. E. Gorfinkel. "Harmonic analysis on spherical homogeneous spaces with solvable stabilizer." Functional Analysis and Its Applications 46, no. 3 (2012): 161–72. http://dx.doi.org/10.1007/s10688-012-0023-3.

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45

Rota, Gian-Carlo. "Harmonic analysis of spherical functions on real reductive groups." Advances in Mathematics 79, no. 1 (1990): 136–37. http://dx.doi.org/10.1016/0001-8708(90)90061-q.

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46

Torta, J. Miquel. "Modelling by Spherical Cap Harmonic Analysis: A Literature Review." Surveys in Geophysics 41, no. 2 (2019): 201–47. http://dx.doi.org/10.1007/s10712-019-09576-2.

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47

Sansò, F. "On the aliasing problem in the spherical harmonic analysis." Journal of Geodesy 64, no. 4 (1990): 313–30. http://dx.doi.org/10.1007/bf02538406.

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48

De Franceschi, G., A. De Santis, and S. Pau. "Ionospheric mapping by regional spherical harmonic analysis: New developments." Advances in Space Research 14, no. 12 (1994): 61–64. http://dx.doi.org/10.1016/0273-1177(94)90240-2.

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49

Sun, Huiyuan, Thushara D. Abhayapala, and Prasanga N. Samarasinghe. "Time Domain Spherical Harmonic Processing with Open Spherical Microphones Recording." Applied Sciences 11, no. 3 (2021): 1074. http://dx.doi.org/10.3390/app11031074.

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Spherical harmonic analysis has been a widely used approach for spatial audio processing in recent years. Among all applications that benefit from spatial processing, spatial Active Noise Control (ANC) remains unique with its requirement for open spherical microphone arrays to record the residual sound field throughout the continuous region. Ideally, a low delay spherical harmonic recording algorithm for open spherical microphone arrays is desired for real-time spatial ANC systems. Currently, frequency domain algorithms for spherical harmonic decomposition of microphone array recordings are ap

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50

Wang, Jian Qiang, Hao Yuan Chen, and Yin Fu Chen. "The Analysis of the Associated Legendre Functions with Non-Integral Degree." Applied Mechanics and Materials 130-134 (October 2011): 3001–5. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.3001.

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Spherical cap harmonic (SCH) theory has been widely used to format regional model of fields that can be expressed as the gradient of a scalar potential. The functions of this method consist of trigonometric functions and associated Legendre functions with integral-order but non-integral degree. Evidently, the constructing and computing of Legendre functions are the core content of the spherical cap functions. In this paper,the approximated calculation method of the normalized association Legendre functions with non-integral degree is introduced and an analysis of the entire order of associated

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