Calculation of Head-Related Transfer Functions for Arbitrary Field Points Using Spherical Harmonics Decomposition

2012 ◽  
Vol 98 (1) ◽  
pp. 72-82 ◽  
Author(s):  
Martin Pollow ◽  
Khoa-Van Nguyen ◽  
Olivier Warusfel ◽  
Thibaut Carpentier ◽  
Markus Müller-Trapet ◽  
...  
Keyword(s):  
Spherical Harmonics ◽  
Transfer Functions ◽  
Arbitrary Field

scholarly journals The FMM-BEM Method for the 3D Particulate Stokes Flow

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Hassib Selmi ◽  
Mohamed Abdelwahed ◽  
Hatem Hamda ◽  
Lassaad El Asmi
Keyword(s):  
Spherical Harmonics ◽  
Stokes Flow ◽  
Transfer Functions ◽  
Stokes Problem ◽  
High Accuracy ◽  
Multipole Moments ◽  
Accuracy Level ◽  
Reasonable Cost

This work introduces new functions based on the spherical harmonics and the solid harmonics which have been used to construct a multipole development for the 3D Stokes problem in order to reduce the operations costs in the BEM method. We show that the major properties of those functions are inherited from the solid harmonics. The contribution of this paper is the introduction of new formulas that serve to calculate the multipole moments and the transfer functions that are necessary for the schemes of orderO(NlogN). Moreover, new translation formulas are introduced to obtain anO(N)scheme. The error truncation of the resulting scheme is discussed. In comparison to the BEM that attains a limit storage atO(104), we present here a method based on FMM-BEM that attains a storage at a limit ofO(106). The implementation of the method achieves a high accuracy level at a reasonable cost.

scholarly journals Assessing Spherical Harmonics Interpolation of Time-Aligned Head-Related Transfer Functions

2021 ◽  
Vol 69 (1/2) ◽  
pp. 104-117
Author(s):  
Johannes M. Arend ◽  
Fabian Brinkmann ◽  
Christoph Pörschmann
Keyword(s):  
Spherical Harmonics ◽  
Transfer Functions

Geologic provinces from unsupervised learning: synthetic experiments in clustering of localized topography/gravity admittance and correlation spectra

2021 ◽  
Author(s):  
Alberto Pastorutti ◽  
Carla Braitenberg
Keyword(s):  
Heat Flow ◽  
Spherical Harmonics ◽  
Transfer Functions ◽  
Flexural Rigidity ◽  
Ground Truth ◽  
Spatial Localization ◽  
Data Set ◽  
Mantle Dynamics ◽  
External Data ◽  
Clustering Model

<p>Partitioning of the Earth surface in "provinces": tectonic domains, outcropping geological units, crustal types, discrete classes extracted from age or geophysical data (e.g. tomography, gravity) is often employed to perform data imputation of ill-sampled observables (e.g. the similarity-based NGHF surface heat flow map [1]) or to constrain the parameters of ill-posed inverse problems (e.g. the gravimetric global Moho model GEMMA [2]).</p><p>We define provinces as noncontiguous areas where quantities or their relationships are similar. Following the goodness metric employed for proxy observables, an adequate province model should be able to significantly improve prediction of the extrapolated quantity. Interpolation of a quantity with no reliance on external data sets a predictivity benchmark, which a province-based prediction should exceed.<br>In a solid Earth modelling perspective, gravity, topography, and their relationship, seem ideal candidates to constrain a province clustering model. Earth gravity and topography, at resolutions of at least 100 km, are known with an incomparable sampling uniformity and negligible error, respect to other observables.</p><p>Most of the observed topography-gravity relationship can be explained by regional isostatic compensation. The topography, representing the load exerted on the lithosphere, is compensated by the elastic, thin-shell like response of the latter. In the spectral domain, flexure results in a lowpass transfer function between topography and isostatic roots. The signal of both surfaces, superimposed, is observed in the gravity field.<br>However, reality shows significant shifts from the ideal case: the separation of nonisostatic effects [3], such as density inhomogeneities, glacial isostatic adjustments, dynamic mantle processes, is nontrivial. Acknowledging this superposition, we aim at identifying clusters of similar topography-gravity transfer functions.</p><p>We evaluate the transfer functions, in the form of admittance and correlation [4], in the spherical harmonics domain. Spatial localization is achieved with the method by Wieczorek and Simons [5], using SHTOOLS [6]. Admittance and correlation spectra are computed on a set of regularly spaced sample points, each point being representative of the topo-gravity relationship in its proximity. The coefficients of the localized topo-gravity admittance and correlation spectra constitute each point features.</p><p>We present a set of experiments performed on synthetic models, in which we can control the variations of elastic parameters and non-isostatic contributions. These tests allowed to define both the feature extraction segment: the spatial localization method and the range of spherical harmonics degrees which are more sensible to lateral variations in flexural rigidity; and the clustering segment: metrics of the ground-truth clusters, performance of dimensionality reduction methods and of different clustering models.</p><p>[1] Lucazeau (2019). Analysis and Mapping of an Updated Terrestrial Heat Flow Data Set. doi:10.1029/2019GC008389<br>[2] Reguzzoni and Sampietro (2015). GEMMA: An Earth crustal model based on GOCE satellite data. doi:10.1016/j.jag.2014.04.002<br>[3] Bagherbandi and Sjöberg (2013). Improving gravimetric–isostatic models of crustal depth by correcting for non-isostatic effects and using CRUST2.0. doi:10.1016/j.earscirev.2012.12.002<br>[4] Simons et al. (1997). Localization of gravity and topography: Constraints on the tectonics and mantle dynamics of Venus. doi:10.1111/j.1365-246X.1997.tb00593.x<br>[5] Wieczorek and Simons (2005). Localized spectral analysis on the sphere. doi:10.1111/j.1365-246X.2005.02687.x<br>[6] Wieczorek and Meschede (2018). SHTools: Tools for Working with Spherical Harmonics. doi:10.1029/2018GC007529</p>

Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

A simple way for producing holographic filters suitable for image improvement

1978 ◽  
Vol 36 (1) ◽  
pp. 226-227
Author(s):  
K.-H. Herrmann ◽  
E. Reuber ◽  
P. Schiske
Keyword(s):  
Transfer Functions ◽  
Diffraction Order ◽  
Lateral Position ◽  
Simple Method ◽  
Spatial Frequencies ◽  
Resolution Electron ◽  
Wiener Filters ◽  
Image Improvement ◽  
Optical Reconstruction ◽  
Set Up

Aposteriori deblurring of high resolution electron micrographs of weak phase objects can be performed by holographic filters [1,2] which are arranged in the Fourier domain of a light-optical reconstruction set-up. According to the diffraction efficiency and the lateral position of the grating structure, the filters permit adjustment of the amplitudes and phases of the spatial frequencies in the image which is obtained in the first diffraction order.In the case of bright field imaging with axial illumination, the Contrast Transfer Functions (CTF) are oscillating, but real. For different imageforming conditions and several signal-to-noise ratios an extensive set of Wiener-filters should be available. A simple method of producing such filters by only photographic and mechanical means will be described here.A transparent master grating with 6.25 lines/mm and 160 mm diameter was produced by a high precision computer plotter. It is photographed through a rotating mask, plotted by a standard plotter.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

Electron Holography Improving Transmission Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 208-209
Author(s):  
Hannes Lichte
Keyword(s):  
Electron Microscopy ◽  
Transfer Functions ◽  
Imaging System ◽  
Spherical Aberration ◽  
Image Plane ◽  
Chromatic Aberration ◽  
Object Wave ◽  
Objective Lens ◽  
Electron Holography ◽  
Wave Aberration

Generally, the electron object wave o(r) is modulated both in amplitude and phase. In the image plane of an ideal imaging system we would expect to find an image wave b(r) that is modulated in exactly the same way, i. e. b(r) =o(r). If, however, there are aberrations, the image wave instead reads as b(r) =o(r) * FT(WTF) i. e. the convolution of the object wave with the Fourier transform of the wave transfer function WTF . Taking into account chromatic aberration, illumination divergence and the wave aberration of the objective lens, one finds WTF(R) = Echrom(R)Ediv(R).exp(iX(R)) . The envelope functions Echrom(R) and Ediv(R) damp the image wave, whereas the effect of the wave aberration X(R) is to disorder amplitude and phase according to real and imaginary part of exp(iX(R)) , as is schematically sketched in fig. 1.Since in ordinary electron microscopy only the amplitude of the image wave can be recorded by the intensity of the image, the wave aberration has to be chosen such that the object component of interest (phase or amplitude) is directed into the image amplitude. Using an aberration free objective lens, for X=0 one sees the object amplitude, for X= π/2 (“Zernike phase contrast”) the object phase. For a real objective lens, however, the wave aberration is given by X(R) = 2π (.25 Csλ3R4 + 0.5ΔzλR2), Cs meaning the coefficient of spherical aberration and Δz defocusing. Consequently, the transfer functions sin X(R) and cos(X(R)) strongly depend on R such that amplitude and phase of the image wave represent only fragments of the object which, fortunately, supplement each other. However, recording only the amplitude gives rise to the fundamental problems, restricting resolution and interpretability of ordinary electron images:

The Effect of Nonlinear Amplitude Growth on the Speech Perception Benefits Provided by a Single-Sided Vocoder

2019 ◽  
Vol 62 (3) ◽  
pp. 745-757 ◽  
Author(s):  
Jessica M. Wess ◽  
Joshua G. W. Bernstein
Keyword(s):  
Transfer Functions ◽  
Spatial Configuration ◽  
Free Field ◽  
Spatial Separation ◽  
Compression And Expansion ◽  
Interaural Difference ◽  
Interaural Differences ◽  
Single Sided Deafness ◽  
Perceptual Separation ◽  
Loudness Growth

PurposeFor listeners with single-sided deafness, a cochlear implant (CI) can improve speech understanding by giving the listener access to the ear with the better target-to-masker ratio (TMR; head shadow) or by providing interaural difference cues to facilitate the perceptual separation of concurrent talkers (squelch). CI simulations presented to listeners with normal hearing examined how these benefits could be affected by interaural differences in loudness growth in a speech-on-speech masking task.MethodExperiment 1 examined a target–masker spatial configuration where the vocoded ear had a poorer TMR than the nonvocoded ear. Experiment 2 examined the reverse configuration. Generic head-related transfer functions simulated free-field listening. Compression or expansion was applied independently to each vocoder channel (power-law exponents: 0.25, 0.5, 1, 1.5, or 2).ResultsCompression reduced the benefit provided by the vocoder ear in both experiments. There was some evidence that expansion increased squelch in Experiment 1 but reduced the benefit in Experiment 2 where the vocoder ear provided a combination of head-shadow and squelch benefits.ConclusionsThe effects of compression and expansion are interpreted in terms of envelope distortion and changes in the vocoded-ear TMR (for head shadow) or changes in perceived target–masker spatial separation (for squelch). The compression parameter is a candidate for clinical optimization to improve single-sided deafness CI outcomes.

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