scholarly journals Spherical harmonic covariance and magnitude function encodings for beamformer design

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yuancheng Luo
Keyword(s):  
Spherical Harmonic ◽  
Acoustic Radiation ◽  
Basis Functions ◽  
Density Functions ◽  
Far Field ◽  
Noise Sources ◽  
Covariance Functions ◽  
Pressure Fields ◽  
Beamformer Design ◽  
Field Response

AbstractMicrophone and speaker array designs have increasingly diverged from simple topologies due to diversity of physical host geometries and use cases. Effective beamformer design must now account for variation in the array’s acoustic radiation pattern, spatial distribution of target and noise sources, and intended beampattern directivity. Relevant tasks such as representing complex pressure fields, specifying spatial priors, and composing beampatterns can be efficiently synthesized using spherical harmonic (SH) basis functions. This paper extends the expansion of common stationary covariance functions onto the SHs and proposes models for encoding magnitude functions on a sphere. Conventional beamformer designs are reformulated in terms of magnitude density functions and beampatterns along SH bases. Applications to speaker far-field response fitting, cross-talk cancelation design, and microphone beampattern fitting are presented.

scholarly journals Study on Acoustic Radiation Calculation and Far Field Criterion of Oil pan

2021 ◽  
Vol 1043 (4) ◽  
pp. 042062
Author(s):  
Yue-zhen Huang ◽  
Bo Zhang ◽  
Ke-lun Zhao ◽  
Xue-bao Xia
Keyword(s):  
Acoustic Radiation ◽  
Far Field ◽  
Field Criterion

Relationships Between Acoustic Radiation Modes, Complex Acoustic Power, and Radiation Efficiency

1997 ◽  
Author(s):  
Pei-Tai Chen
Keyword(s):  
Acoustic Radiation ◽  
Acoustic Power ◽  
Radiation Efficiency ◽  
Acoustic Energy ◽  
Normal Velocity ◽  
Far Field ◽  
Surface Complex ◽  
Surface Integral ◽  
Complex Power ◽  
Mass Spring

Abstract The paper explores the physical meaning underlying the surface complex acoustic power of a vibrating body, and its relationship to radiation efficiency under mono-frequency oscillations. The vibrating can be the entire wetted surface, or only a part of the surface with the remaining surface being held rigid. The surface complex acoustic power can be computed by the surface integral of pressure multiplying the complex conjugate of normal velocity. Based on the Gaussian Divergence theorem, it is shown that the real part of the complex power is the power radiated into a far field, while that the imaginary part pertains to the volume integral of the difference between the acoustic kinetic energy density with the potential energy density over the volume between the vibrating surface and the far field. The dynamical behavior of the acoustic field can be viewed as an infinite degree of freedom mass/spring/dashpot system, where the mass and spring are the inertia effects and acoustic compression effects of the acoustic particles and the dashpot is due to the plane wave relationship of the pressure waves at the far field that the acoustic energy propagates away from the acoustic field. By the model of the mass /spring/dashpot system, the phase angle of the complex acoustic power is identified as an indication of the ability of the vibrating surface to radiate acoustic power. The phase angle of the complex power depends on the distribution of the surface normal velocity. In order to study the normal velocity profile in relation to the ability to radiate acoustic energy, the previously established radiation mode (Chen and Ginsberg, 1995) is introduced and extended to situations in which a part of the surface is held rigid. An orthogonal condition for the velocity radiation modes is also established such that arbitrary velocity profiles can be decomposed into radiation modes. The acoustic modal radiation efficiency, defined as the radiated modal acoustic power divided by the surface integral of mean square normal velocity, is investigated in terms of the acoustic eigenvalue of that mode. Several different geometries of vibrating bodies are used to demonstrate the correlation of radiation efficiencies to eigenvalues of radiation modes, which include a rectangular baffled vibrating membrane, a box with only one of the six surfaces vibrating, a slender spheroidal body, and a spherical body. This correlation of acoustic radiation characteristics for different geometries is also demonstrated for a spheroidal body vibrating at some areas with other areas being held rigid.

Gravity Field Recovery and Observation Noise Separation from Simultaneous Laser Ranging Interferometer and K-Band Ranging System Measurements

2020 ◽  
Author(s):  
Andreas Kvas ◽  
Saniya Behzadpour ◽  
Torsten Mayer-Guerr
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Uncertainty Propagation ◽  
Stochastic Modelling ◽  
Laser Ranging ◽  
Polar Regions ◽  
Data Types ◽  
Covariance Functions ◽  
Gravity Field Recovery ◽  
K Band

<p>The unique instrumentation of GRACE Follow-On (GRACE-FO) offers two independent inter-satellite ranging systems with concurrent observations. Next to a K-Band Ranging System (KBR), which has already been proved during the highly-successfully GRACE mission, the GRACE-FO satellites are equipped with an experimental Laser Ranging Interferometer (LRI), which features a drastically increased measurement precision compared to the KBR. Having two simultaneous ranging observations available allows for cross-calibration between the instruments and, to some degree, the separation of ranging noise from other sources such as noise in the on-board accelerometer (ACC) measurements.  </p> <p>In this contribution we present a stochastic description of the two ranging observation types provided by GRACE-FO, which also takes cross-correlations between the two observables into account. We determine the unknown noise covariance functions through variance component estimation and show that this method is, to some extent, capable of separating between KBR, LRI, and ACC noise. A side effect of this stochastic modelling is that the formal errors of the spherical harmonic coefficients fit very well to empirical estimates, which is key for combination with other data types and uncertainty propagation. We further compare the gravity field solutions obtained from a combined least-squares adjustment to KBR-only and LRI-only results and discuss the differences between the time series with a focus on gravity field and calibration parameters. Even though, at the moment, global statistics only show a minor improvement when using LRI ranging measurements instead of KBR observations, some parts of the spectrum and geographic regions benefit significantly from the increased measurement accuracy of the LRI. Specifically, we see a higher signal-to-noise ratio in low spherical harmonic orders and the polar regions.</p>

WAVELET-BASED POSTPROCESSING OF JET LES DATA FOR ACOUSTIC FAR-FIELD EXTRAPOLATIONS

2013 ◽  
Vol 21 (04) ◽  
pp. 1350017
Author(s):  
RAMIN KAVIANI ◽  
VAHID ESFAHANIAN ◽  
MOHAMMAD EBRAHIMI
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Near Field ◽  
Flow Simulation ◽  
Computational Time ◽  
Jet Flows ◽  
Small Scale ◽  
Frequency Noise ◽  
Far Field ◽  
Noise Sources

The affordable grid resolutions in conventional large-eddy simulations (LESs) of high Reynolds jet flows are unable to capture the sound generated by fluid motions near and beyond the grid cut-off scale. As a result, the frequency spectrum of the extrapolated sound field is artificially truncated at high frequencies. In this paper, a new method is proposed to account for the high frequency noise sources beyond the resolution of a compressible flow simulation. The large-scale turbulent structures as dominant radiators of sound are captured in LES, satisfying filtered Navier–Stokes equations, while for small-scale turbulence, a Kolmogorov's turbulence spectrum is imposed. The latter is performed via a wavelet-based extrapolation to add randomly generated small-scale noise sources to the LES near-field data. Further, the vorticity and instability waves are filtered out via a passive wavelet-based masking and the whole spectrum of filtered data are captured on a Ffowcs-Williams/Hawkings (FW-H) surface surrounding the near-field region and are projected to acoustic far-field. The algorithm can be implemented as a separate postprocessing stage and it is observed that the computational time is considerably reduced utilizing a hybrid of many-core and multi-core framework, i.e. MPI-CUDA programming. The comparison of the results obtained from this procedure and those from experiments for high subsonic and transonic jets, shows that the far-field noise spectrum agree well up to 2 times of the grid cut-off frequency.

Sign in / Sign up

Export Citation Format

Share Document