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We derive a compressive sampling method for acoustic field reconstruction using field measurements on a pre-defined spherical grid that has theoretically guaranteed relations between signal sparsity, measurement number, and reconstruction accuracy. This method can be used to reconstruct band limited spherical harmonic or Wigner D-function series (spherical harmonic series are a special case) with sparse coefficients. Contrasting typical compressive sampling methods for Wigner D-function series that use arbitrary random measurements, the new method samples randomly on an equiangular grid, a practical and commonly used sampling pattern. Using its periodic extension, we transform the reconstruction of a Wigner D-function series into a multi-dimensional Fourier domain reconstruction problem. We establish that this transformation has a bounded effect on sparsity level and provide numerical studies of this effect. We also compare the reconstruction performance of the new approach to classical Nyquist sampling and existing compressive sampling methods. In our tests, the new compressive sampling approach performs comparably to other guaranteed compressive sampling approaches and needs a fraction of the measurements dictated by the Nyquist sampling theorem. Moreover, using one-third of the measurements or less, the new compressive sampling method can provide over 20 dB better de-noising capability than oversampling with classical Fourier theory. [ABSTRACT FROM AUTHOR]

Current standards for the measurement of impulse noise (e.g., MIL-STD-1474E) recommend using a sampling rate of at least 200 kHz in order to accurately estimate the risk of hearing damage. The given motivation for this high sampling rate is to ensure a temporal resolution in the impulse waveform fine enough to accurately capture the peak pressure. However, the Nyquist-Shannon sampling theorem specifies that a sampled signal can accurately reconstruct both the amplitude and phase information of a signal given the sampling rate is at least twice the highest frequency present in the original signal. Thus, it is possible to reconstruct a band limited signal with the same temporal resolution as one captured at a higher sampling rate if the contributions of energy above the Nyquist rate can be ignored. In this study, resampling techniques are applied to a signal sampled at 48 kHz to extract A-weighted sound pressure energy estimates within 0.1 dB of those obtained at a higher sampling rate. Our results suggest sampling rates for impulsive noise should be based on the range of frequencies expected to make a contribution to injury risk rather than on concerns about temporal resolution. [ABSTRACT FROM AUTHOR]

The past decades have witnessed great efforts in the on-demand ultrasonic field design in which the time reversal technology was widely used in the whole-space acoustic hologram. In practice, the acoustic field of interest is usually bounded in a finite region with flexible distribution. Here, the use of prolate spheroidal wave functions to generate an arbitrary ultrasonic field in a finite region is proposed. The prolate spheroidal functions, which form a complete set of band limited functions and are orthogonal in the infinite and finite regions, can be efficiently reconstructed by the sampling theorem. To display the validation of the proposed method, two types of functional ultrasonic fields are numerically simulated. One type is the ultrasound standing wave field for which six nodes and two nodes are separately realized for two different types of standing waves in the limited range of (− 2 λ , 2 λ). In addition, a composite standing wave field is stimulated with more complicated nodal distributions. The other type is the ultrasound focusing field, where three focal spots with the mainlobe sizes of λ , 0.5 λ , and 0.35 λ are demonstrated. It is worth noting that the nontrivial side lobes for super-oscillation focusing are designed to be about 3 λ away from the central focal spot (the mainlobe size 0.35 λ). This work has much significance in the applications of acoustic tweezing, ultrasonic imaging, and treatment. [ABSTRACT FROM AUTHOR]

A semi-coprime array (SCA) interleaves two undersampled uniform linear arrays (ULAs) and a Q-element standard ULA. The undersampling factors of the first two arrays are QM and QN, respectively, where M and N are coprime. The resulting non-ULA is highly sparse. Taking the minimum of the absolute values of the conventional beampatterns of the three arrays results in a beampattern that is free of grating lobes. A SCA requires fewer sensors than other popular sparse arrays such as coprime arrays, nested arrays, and minimum redundant arrays for a given aperture. Also, a SCA exhibits better side lobe patterns than other sparse arrays. This means that a SCA is better able to mask signals away from the look direction and detect weak sources in the presence of strong interferers. In this paper, the author explores the direction of arrival estimation with the SCA. The results illustrate the SCA's ability to reduce the number of sensors and decrease system cost and complexity in various signal processing applications. [ABSTRACT FROM AUTHOR]

Suitable data for spatial wave field analyses in concert halls need to satisfy the sampling theorem and hence requires densely spaced measurement positions over extended regions. The described measurement apparatus is capable of automatically sampling the sound field in auditoria over a surface of 5.30 m × 8.00 m to any appointed resolutions. In addition to discussing design features, a case study based on measured impulse responses is presented. The experimental data allow wave field animations demonstrating how sound propagating at grazing incidence over theater seating is scattered from rows of chairs (seat-dip effect). The visualized data of reflections and scattering from an auditorium's boundaries give insights and opportunities for advanced analyses. [ABSTRACT FROM AUTHOR]

Coprime linear microphone arrays allow for narrower beams with fewer sensors. A coprime microphone array consists of two staggered uniform linear subarrays with M and N microphones, where M and N are coprime with each other. By applying spatial filtering to both subarrays and combining their outputs, M + N - 1 microphones yield M N directional bands. In this work, the coprime sampling theory is implemented in the form of a linear microphone array of 16 elements with coprime numbers of 9 and 8. This coprime microphone array is experimentally tested to validate the coprime array theory. Both predicted and measured results are discussed. Experimental results confirm that narrow beampatterns as predicted by the coprime sampling theory can be obtained by the coprime microphone array. [ABSTRACT FROM AUTHOR]

Ground reflections cause problems when estimating the direction of arrival of aircraft noise. In traditional methods, based on the time differences between the microphones of a compact array, they may cause a significant loss of accuracy in the vertical direction. This study evaluates the use of first-order directional microphones, instead of omnidirectional, with the aim of reducing the amplitude of the reflected sound. Such a modification allows the problem to be treated as in free field conditions. Although further tests are needed for a complete evaluation of the method, the experimental results presented here show that under the particular conditions tested the vertical angle error is reduced ~10° for both jet and propeller aircraft by selecting an appropriate directivity pattern. It is also shown that the final level of error depends on the vertical angle of arrival of the sound, and that the estimates of the horizontal angle of arrival are not influenced by the directivity pattern of the microphones nor by the reflective properties of the ground. [ABSTRACT FROM AUTHOR]