The Experts below are selected from a list of 39597 Experts worldwide ranked by ideXlab platform
Deep Sen - One of the best experts on this subject based on the ideXlab platform.
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error analysis of Spherical Harmonic soundfield representations in terms of truncation and aliasing errors
International Conference on Acoustics Speech and Signal Processing, 2013Co-Authors: Stefanie Brown, Deep SenAbstract:The use of the Spherical Harmonic representation of a soundfield is useful when attempting to record, reproduce or manipulate the spatial qualities of the soundfield. However, the practical requirement of discrete sampling in the spatial domain brings errors to the system, namely those of truncation and spatial aliasing. The truncation error can be seen in the synthesized pressure, while spatial aliasing is apparent when looking at the Spherical Harmonic coefficients themselves. These errors are linked to each other through the number and position of the microphones in the array, as well as the method used to perform numerical integration on the sphere, but they can exist separately. This paper discusses the above topics and investigates two approaches to numerical integration in regards to sampling the soundfield using an em32 Eigenmike® microphone array.
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analysis of the Sphericalwave truncation error for Spherical Harmonic soundfield expansions
International Conference on Acoustics Speech and Signal Processing, 2012Co-Authors: Stefanie Brown, Shuai Wang, Deep SenAbstract:Three dimensional soundfield recording and reproduction is an area of ongoing investigation and its implementation is increasingly achieved through use of the infinite Spherical Harmonic soundfield expansion. Perfect recording or reconstruction requires infinite microphones or loudspeakers, respectively. Thus, real-world approximations to both require spatial discretisation, which truncates the soundfield expansion and loses some of the soundfield information. The resulting truncation error is the focus of this paper, specifically for soundfields comprising of Spherical waves. We define two norms of the truncation error to signal ratio, L 2 and L ∞ , for comparison and use in different situations. Finally we observe how some of these errors converge to the plane wave case under certain circumstances.
Christopher Jekeli - One of the best experts on this subject based on the ideXlab platform.
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on the computation and approximation of ultra high degree Spherical Harmonic series
Journal of Geodesy, 2007Co-Authors: Christopher Jekeli, Jong Ki Lee, Jay H KwonAbstract:Spherical Harmonic series, commonly used to represent the Earth’s gravitational field, are now routinely expanded to ultra-high degree (> 2,000), where the computations of the associated Legendre functions exhibit extremely large ranges (thousands of orders) of magnitudes with varying latitude. We show that in the degree-and-order domain, (l,m), of these functions (with full ortho-normalization), their rather stable oscillatory behavior is distinctly separated from a region of very strong attenuation by a simple linear relationship: \(m = \ell \sin \theta\), where θ is the polar angle. Derivatives and integrals of associated Legendre functions have these same characteristics. This leads to an operational approach to the computation of Spherical Harmonic series, including derivatives and integrals of such series, that neglects the numerically insignificant functions on the basis of the above empirical relationship and obviates any concern about their broad range of magnitudes in the recursion formulas that are used to compute them. Tests with a simulated gravitational field show that the errors in so doing can be made less than the data noise at all latitudes and up to expansion degree of at least 10,800. Neglecting numerically insignificant terms in the Spherical Harmonic series also offers a computational savings of at least one third.
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an analysis of vertical deflections derived from high degree Spherical Harmonic models
Journal of Geodesy, 1999Co-Authors: Christopher JekeliAbstract:The theoretical differences between the Helmert deflection of the vertical and that computed from a truncated Spherical Harmonic series of the gravity field, aside from the limited spectral content in the latter, include the curvature of the normal plumb line, the permanent tidal effect, and datum origin and orientation offsets. A numerical comparison between deflections derived from Spherical Harmonic model EGM96 and astronomic deflections in the conterminous United States (CONUS) shows that correcting these systematic effects reduces the mean differences in some areas. Overall, the mean difference in CONUS is reduced from −0.219 arcsec to −0.058 arcsec for the south–north deflection, and from +0.016 arcsec to +0.004 arcsec for the west–east deflection. Further analysis of the root-mean-square differences indicates that the high-degree spectrum of the EGM96 model has significantly less power than implied by the deflection data.
Benjamin D Wandelt - One of the best experts on this subject based on the ideXlab platform.
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fast and exact spin s Spherical Harmonic transforms
Astrophysical Journal Supplement Series, 2010Co-Authors: K M Huffenberger, Benjamin D WandeltAbstract:We demonstrate a fast spin-s Spherical Harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the computation of several distinct spin transforms simultaneously. Specifically, only one set of special functions is computed for transforms of quantities with any spin, namely the Wigner d matrices evaluated at π/2, which may be computed with efficient recursions. For any spin, the computation scales as , where L is the band limit of the function. Our publicly available numerical implementation permits very high accuracy at modest computational cost. We discuss applications to the cosmic microwave background and gravitational lensing.
Stefanie Brown - One of the best experts on this subject based on the ideXlab platform.
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error analysis of Spherical Harmonic soundfield representations in terms of truncation and aliasing errors
International Conference on Acoustics Speech and Signal Processing, 2013Co-Authors: Stefanie Brown, Deep SenAbstract:The use of the Spherical Harmonic representation of a soundfield is useful when attempting to record, reproduce or manipulate the spatial qualities of the soundfield. However, the practical requirement of discrete sampling in the spatial domain brings errors to the system, namely those of truncation and spatial aliasing. The truncation error can be seen in the synthesized pressure, while spatial aliasing is apparent when looking at the Spherical Harmonic coefficients themselves. These errors are linked to each other through the number and position of the microphones in the array, as well as the method used to perform numerical integration on the sphere, but they can exist separately. This paper discusses the above topics and investigates two approaches to numerical integration in regards to sampling the soundfield using an em32 Eigenmike® microphone array.
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analysis of the Sphericalwave truncation error for Spherical Harmonic soundfield expansions
International Conference on Acoustics Speech and Signal Processing, 2012Co-Authors: Stefanie Brown, Shuai Wang, Deep SenAbstract:Three dimensional soundfield recording and reproduction is an area of ongoing investigation and its implementation is increasingly achieved through use of the infinite Spherical Harmonic soundfield expansion. Perfect recording or reconstruction requires infinite microphones or loudspeakers, respectively. Thus, real-world approximations to both require spatial discretisation, which truncates the soundfield expansion and loses some of the soundfield information. The resulting truncation error is the focus of this paper, specifically for soundfields comprising of Spherical waves. We define two norms of the truncation error to signal ratio, L 2 and L ∞ , for comparison and use in different situations. Finally we observe how some of these errors converge to the plane wave case under certain circumstances.
Christian Hirt - One of the best experts on this subject based on the ideXlab platform.
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Divergence-free Spherical Harmonic gravity field modelling based on the Runge–Krarup theorem: a case study for the Moon
Journal of Geodesy, 2019Co-Authors: Blažej Bucha, Christian Hirt, Michael KuhnAbstract:Recent numerical studies on external gravity field modelling show that external Spherical Harmonic series may diverge near or on planetary surfaces. This paper investigates an alternative solution that is still based on external Spherical Harmonic series, but capable of avoiding the divergence effect. The approach relies on the Runge–Krarup theorem and the iterative downward continuation. In theory, Runge–Krarup-type solutions are able to approximate the true potential within the entire space external to the masses with an arbitrary $$\varepsilon $$ ε -accuracy, $$\varepsilon >0$$ ε > 0 . Using gravity implied by the lunar topography, we show numerically that this technique avoids indeed the divergence effect, at least at the studied 5 arc-min resolution. In the context of the iterative scheme, we show that a function expressed as a truncated solid Spherical Harmonic expansion on a general star-shaped surface possesses an infinite surface Spherical Harmonic spectrum after it is mapped onto a sphere. We also study the convergence of the gradient approach, which is a technique for efficient grid-wise synthesis on irregular surfaces. We show that the resulting Taylor series may converge slowly when analytically upward continuing from points inside the masses. The continuation from the mass-free space should therefore be preferred. As an underlying topic of the paper, Spherical Harmonic coefficients from spectral gravity forward modelling and their Runge–Krarup counterpart are numerically studied. Regarding their different nature, we formulate some research topics that might contribute to a deeper understanding of the current methodologies used to develop combined high-degree Spherical Harmonic gravity models.
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prediction of vertical deflections from high degree Spherical Harmonic synthesis and residual terrain model data
Journal of Geodesy, 2010Co-Authors: Christian HirtAbstract:This study demonstrates that in mountainous areas the use of residual terrain model (RTM) data significantly improves the accuracy of vertical deflections obtained from high-degree Spherical Harmonic synthesis. The new Earth gravitational model EGM2008 is used to compute vertical deflections up to a Spherical Harmonic degree of 2,160. RTM data can be constructed as difference between high-resolution Shuttle Radar Topography Mission (SRTM) elevation data and the terrain model DTM2006.0 (a Spherical Harmonic terrain model that complements EGM2008) providing the long-wavelength reference surface. Because these RTM elevations imply most of the gravity field signal beyond Spherical Harmonic degree of 2,160, they can be used to augment EGM2008 vertical deflection predictions in the very high Spherical Harmonic degrees. In two mountainous test areas—the German and the Swiss Alps—the combined use of EGM2008 and RTM data was successfully tested at 223 stations with high-precision astrogeodetic vertical deflections from recent zenith camera observations (accuracy of about 0.1 arc seconds) available. The comparison of EGM2008 vertical deflections with the ground-truth astrogeodetic observations shows root mean square (RMS) values (from differences) of 3.5 arc seconds for ξ and 3.2 arc seconds for η, respectively. Using a combination of EGM2008 and RTM data for the prediction of vertical deflections considerably reduces the RMS values to the level of 0.8 arc seconds for both vertical deflection components, which is a significant improvement of about 75%. Density anomalies of the real topography with respect to the residual model topography are one factor limiting the accuracy of the approach. The proposed technique for vertical deflection predictions is based on three publicly available data sets: (1) EGM2008, (2) DTM2006.0 and (3) SRTM elevation data. This allows replication of the approach for improving the accuracy of EGM2008 vertical deflection predictions in regions with a rough topography or for improved validation of EGM2008 and future high-degree Spherical Harmonic models by means of independent ground truth data.
