arXiv subjects

Wolfgang Kreuzer

Publications and source records attributed to Wolfgang Kreuzer.

9 recordsLinked to original sources

arXiv2026

Echo Detection in Spatial Room Impulse Responses Measured with Spherical Microphone Arrays Using the Herglotz Wavefunction

Early reflections in spatial room impulse responses (SRIRs) measured using spherical microphone arrays (SMAs) play an important role in spatial audio analysis, rendering, and reverberation modeling. Their accurate localization and characterization can facilitate the analysis, processing, and manipulation of measured reverberation fields. This paper proposes a method for detecting and characterizing early reflections based on the Herglotz wavefunction formalism. The measured sound field is represented as a continuous superposition of incident plane waves, from which a localization function is derived in the spherical harmonic domain. An adaptive radial Gaussian fitting procedure is then used to estimate both the directions of arrival (DoAs) and the number of incident reflections within a single analysis frame. The proposed framework is evaluated using simulated and measured SRIRs and compared with conventional steered response power (SRP) and multiple signal classification (MUSIC) localization methods. The results demonstrate improved localization accuracy and more reliable detection of multiple simultaneous reflections, highlighting the potential of the proposed Herglotz-based formulation for the analysis of early reflections in SMA-measured SRIRs.

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arXiv2026

Effect of different clustering approaches on the multilevel fast multipole method for the Helmholtz equation

The fast multipole method (FMM) is an important component for the boundary element method (BEM), because with the FMM the efficiency and feasibility of the BEM can be enhanced to a large degree. Part of the FMM is grouping the elements of the boundary element mesh into different clusters. The size of these clusters in terms of number of elements and spatial expansion has a huge impact on the efficiency and stability of the method. However, while the theory behind the multipole expansion has been broadly researched, the clustering process itself and its effect on the FMM has been neglected in comparison. Most of the time, for example, it is implicitly assumed that the elements of the mesh have about the same size, which is often not the case in practical applications, e.g., when calculating the sound field around the human head. In this study we compare different types of clustering approaches with respect to stability and efficiency of the underlying FMM applied to meshes that have uniform as well as non-uniform element sizes. Also, some examples are provided for cases where a wrong clustering can lead to numerical problems and instabilities of the FMM-BEM.

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arXiv2026

Localizing broadband noise sources using the Loève spectrum and a 2.5D approach

The localization of moving sound sources using a microphone array is typically based on modifying the signal to compensate for the Doppler effect. In the time domain this compensation is done on a sample-by-sample basis. In the frequency domain short time segments need to be used in which the Doppler effect is assumed to be approximately constant and a discrete Fourier transform is done on each segment. In contrast, the authors developed an inverse 2.5D localization method for uniformly moving single-frequency sources that works in the spectral domain and allows for the use of longer windows. This was achieved by modifying the 2.5D forward model to directly compute the effect of the motion in the static observer position. The method does neither require to modify the measured signal nor does it require quasi-stationary of the measurements within the window used. Unfortunately, this approach is not directly suitable for broad-band stochastic sources, and in the present work we will investigate how the statistical properties of a uniformly moving stochastic source change when observed at a static observer. Using a 2.5D setting, the relation between the power spectral density of the moving source and the Loève spectrum, which is a generalization of the cross-spectral density at the static receivers, was derived. Based on simulated data with speeds up to 100 m\,s$^{-1}$, the work presented here provides a proof of concept for a method based on multi-taper estimates for the Loève spectrum to localize moving broad-band stochastic sources . Currently, the method requires a stationary source signal and that the spectral density is flat within a certain range around the frequency of interest. Also, correlations between sources are currently not considered.

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arXiv2024

NumCalc: An open source BEM code for solving acoustic scattering problems

The calculation of the acoustic field in or around objects is an important task in acoustic engineering. To numerically solve this task, the boundary element method (BEM) is a commonly used method especially for infinite domains. The open source tool Mesh2HRTF and its BEM core NumCalc provide users with a collection of free software for acoustic simulations without the need of having an in-depth knowledge into numerical methods. However, we feel that users should have a basic understanding with respect to the methods behind the software they are using. We are convinced that this basic understanding helps in avoiding common mistakes and also helps to understand the requirements to use the software. To provide this background is the first motivation for this paper. A second motivation for this paper is to demonstrate the accuracy of NumCalc when solving benchmark problems. Thus, users can get an idea about the accuracy they can expect when using NumCalc as well as the memory and CPU requirements of NumCalc. A third motivation for this paper is to give users detailed information about some parts of the actual implementation that are usually not mentioned in literature, e.g., the specific version of the fast multipole method and its clustering process or how to use frequency-dependent admittance boundary conditions.

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arXiv2024

Localizing uniformly moving single-frequency sources using an inverse 2.5D approach

Localizing linearly moving sound sources using microphone arrays is challenging as the transient nature of the signal leads to relatively short observation periods. Commonly, a moving focus is used and most methods operate at least partially in the time domain. In contrast, this manuscript presents an inverse source localization algorithm for uniformly moving single-frequency sources that acts entirely in the frequency domain. For this, a 2.5D approach is utilized and a transfer function between sources and a microphone grid is derived. By solving a least squares problem using the data at the microphone grid, the unknown source distribution in the moving frame can be determined. First, the time signals need to be transformed from time into frequency domain using a windowed discrete Fourier transform (DFT), which leads to spectral leakage that depends on the length of the time interval and the analysis window used. To include spectral leakage in the numerical model, the calculation of the transfer matrix is modified using the Fourier transform of the analysis window in the DFT applied to the measurements. Currently, this approach is limited to single-frequency sources as this restriction allows for simplified calculations and reduces the computational effort. The least squares problem is solved using a Tikhonov regularization and an L-curve approach. As moving sources are considered, utilizing the Doppler effect enhances the stability of the system by combining the transfer functions for multiple frequencies in the measured signals. The performance is validated using simulated data of a moving point source with or without a reflecting ground. Numerical experiments are performed to show the effect of the choice of frequencies in the receiver spectrum, the effect of the DFT, the source frequency, the distance between source and receiver, and the robustness with respect to noise.

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arXiv2024

About the Burton-Miller factor in the low frequency region

The Burton-Miller method is a widely used approach in acoustics to enhance the stability of the boundary element method for exterior Helmholtz problems at so-called critical frequencies. This method depends on a coupling parameter $η$ and it can be shown that as long as $η$ has an imaginary part different from 0, the boundary integral formulation for the Helmholtz equation has a unique solution at all frequencies. A popular choice for this parameter is $η= \frac{\mathrm{i}}{k}$, where $k$ is the wavenumber. It can be shown that this choice is quasi optimal, at least in the high frequency limit. However, especially in the low frequency region, where the critical frequencies are still sparsely distributed, different choices for this factor result in a smaller condition number and a smaller error of the solution. In this work, alternative choices for this factor are compared based on numerical experiments. Additionally, a way to enhance the Burton-Miller solution with $η= \frac{\mathrm{i}}{k}$ for a sound hard scatterer in the low frequency region by an additional step of a modified Richardson iteration is introduced.

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arXiv2022

Numerical simulation of sound propagation in and around ducts using thin boundary elements

Investigating the sound field in and around ducts is an important topic in acoustics, e.g. when simulating musical instruments or the human vocal tract. In this paper a method that is based on the boundary element method in 3D combined with a formulation for infinitely thin elements is presented. The boundary integral equations for these elements are presented, and numerical experiments are used to illustrate the behavior of the thin elements. Using the example of a closed benchmark duct, boundary element solutions for thin elements and surface elements are compared with the analytic solution, and the accuracy of the boundary element method as function of element size is investigated. As already shown for surface elements in the literature, an accumulation of the error along the duct can also be found for thin elements, but in contrast to surface elements this effect is not as big and a damping of the amplitude cannot be seen. In a second experiment, the impedance at the open end of a half open duct is compared with formulas for the radiation impedance of an unflanged tube, and a good agreement is shown. Finally, resonance frequencies of a tube open at both ends are calculated and compared with measured spectra. For sufficiently small element sizes frequencies for lower harmonics agree very well, for higher frequencies a difference of a few Hertz can be observed, which may be explained by the fact that the method does not consider dampening effects near the duct walls. The numerical experiments also suggest, that for duct simulations the usual six to eight elements per wavelength rule is not enough for accurate results.

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arXiv2018

Using B-spline frames to approximate solutions of acoustic scattering problems

Although frames, which are a generalization of bases, are important tools used in signal processing, their potential in other fields of engineering and applied mathematics (e.g. acoustics) has not been fully explored yet. Gabor frames, that are specific type of frames, are very well adapted to oscillating functions, and therefore have a great potential to efficiently represent functions in connection with the Helmholtz operator. In this paper representations of the solution of a scattering problem in 2D using Gabor frames based on B-splines as building blocks are investigated. Practical issues concerning the implementation of frames like the restriction of the frame elements to a finite interval and methods to determine the unknown coefficients for the representation, i.e. by using dual frames or by solving a least squares problem, are discussed. Numerical experiments are made comparing the different ways to determine the unknown expansion coefficients and the representations are compared in terms of their efficiency, i.e. the number of used frame coefficients versus the accuracy of the approximation. In all cases the coefficients calculated with a slightly modified orthogonal matching pursuit algorithm provide the best accuracy versus sparsity ratio.

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arXiv2016

A-priori mesh grading for the numerical calculation of the head-related transfer functions

Head-related transfer functions (HRTFs) describe the directional filtering of the incoming sound caused by the morphology of a listener's head and pinnae. When an accurate model of a listener's morphology exists, HRTFs can be calculated numerically with the boundary element method (BEM). However, the general recommendation to model the head and pinnae with at least six elements per wavelength renders the BEM as a time-consuming procedure when calculating HRTFs for the full audible frequency range. In this study, a mesh preprocessing algorithm is proposed, viz., a-priori mesh grading, which reduces the computational costs in the HRTF calculation process significantly. The mesh grading algorithm deliberately violates the recommendation of at least six elements per wavelength in certain regions of the head and pinnae and varies the size of elements gradually according to an a-priori defined grading function. The evaluation of the algorithm involved HRTFs calculated for various geometric objects including meshes of three human listeners and various grading functions. The numerical accuracy and the predicted sound-localization performance of calculated HRTFs were analyzed. A-priori mesh grading appeared to be suitable for the numerical calculation of HRTFs in the full audible frequency range and outperformed uniform meshes in terms of numerical errors, perception based predictions of sound-localization performance, and computational costs.

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