An objective measure for the sensitivity of room impulse response and its link to a diffuse sound field.

This study is relevant to acoustic measurements in reverberation rooms such as measurements of sound transmission, sound absorption, and sound power levels of noise sources. The study presents a quantitative measure for the diffuseness in a room, which is first introduced theoretically and subsequently examined experimentally. The sensitivity of a room due to changes in the initial conditions is quantified by measuring a pair of impulse responses in a room differing only in the sound source position. Such changes are linked to mixing and the diffuse sound field. The measure is based on the maximum of the absolute value of the cross-correlation between the time windowed sections of the two impulse responses. By integrating this quantity normalized by the energy of the impulse response of the room, a single number rating is obtained. Results based on three sets of experiments indicate that the diffusers and absorbers in the room influence the proposed sensitivity measures systematically.

Conservation of power of the supersonic acoustic intensity.

The supersonic intensity is a quantity that represents the net acoustic output that a source couples into the medium; it can be regarded as a spatially low-pass filtered version of the active intensity. This spatial filtering can lead to significant error due to spatial truncation. In this paper, based on a space-domain formulation of the problem, the finite aperture error is analyzed and examined experimentally. The results indicate that the finite aperture error can be mitigated with the appropriate processing and that the supersonic intensity provides a valid quantitative representation of the effective radiation of acoustic sources.

Deconvolution for the localization of sound sources using a circular microphone array.

During the last decade, the aeroacoustic community has examined various methods based on deconvolution to improve the visualization of acoustic fields scanned with planar sparse arrays of microphones. These methods assume that the beamforming map in an observation plane can be approximated by a convolution of the distribution of the actual sources and the beamformer's point-spread function, defined as the beamformer's response to a point source. By deconvolving the resulting map, the resolution is improved, and the side-lobes effect is reduced or even eliminated compared to conventional beamforming. Even though these methods were originally designed for planar sparse arrays, in the present study, they are adapted to uniform circular arrays for mapping the sound over 360°. This geometry has the advantage that the beamforming output is practically independent of the focusing direction, meaning that the beamformer's point-spread function is shift-invariant. This makes it possible to apply computationally efficient deconvolution algorithms that consist of spectral procedures in the entire region of interest, such as the deconvolution approach for the mapping of the acoustic sources 2, the Fourier-based non-negative least squares, and the Richardson-Lucy. This investigation examines the matter with computer simulations and measurements.

Combination of acoustical radiosity and the image source method.

A combined model for room acoustic predictions is developed, aiming to treat both diffuse and specular reflections in a unified way. Two established methods are incorporated: acoustical radiosity, accounting for the diffuse part, and the image source method, accounting for the specular part. The model is based on conservation of acoustical energy. Losses are taken into account by the energy absorption coefficient, and the diffuse reflections are controlled via the scattering coefficient, which defines the portion of energy that has been diffusely reflected. The way the model is formulated allows for a dynamic control of the image source production, so that no fixed maximum reflection order is required. The model is optimized for energy impulse response predictions in arbitrary polyhedral rooms. The predictions are validated by comparison with published measured data for a real music studio hall. The proposed model turns out to be promising for acoustic predictions providing a high level of detail and accuracy.

Experimental validation of sound field control with a circular double-layer array of loudspeakers.

This paper is concerned with experimental validation of a recently proposed method of controlling sound fields with a circular double-layer array of loudspeakers [Chang and Jacobsen, J. Acoust. Soc. Am. 131(6), 4518-4525 (2012)]. The double-layer of loudspeakers is realized with 20 pairs of closed-box loudspeakers mounted back-to-back. Source strengths are obtained with several solution methods by modeling loudspeakers as a weighted combination of monopoles and dipoles. Sound pressure levels of the controlled sound fields are measured inside and outside the array in an anechoic room, and performance indices are calculated. The experimental results show that a method of combining pure contrast maximization with a pressure matching technique provides only a small error in the listening zone between the desired and the reproduced fields, and at the same time reduces the sound level in the quiet zone as expected in the simulation studies well above the spatial Nyquist frequency except at a few frequencies. It is also shown that errors in the positions of the loudspeakers can be critical to the results at frequencies where the distance between the inner and the outer array is close to half a wavelength.

Sound field separation with sound pressure and particle velocity measurements.

In conventional near-field acoustic holography (NAH) it is not possible to distinguish between sound from the two sides of the array, thus, it is a requirement that all the sources are confined to only one side and radiate into a free field. When this requirement cannot be fulfilled, sound field separation techniques make it possible to distinguish between outgoing and incoming waves from the two sides, and thus NAH can be applied. In this paper, a separation method based on the measurement of the particle velocity in two layers and another method based on the measurement of the pressure and the velocity in a single layer are proposed. The two methods use an equivalent source formulation with separate transfer matrices for the outgoing and incoming waves, so that the sound from the two sides of the array can be modeled independently. A weighting scheme is proposed to account for the distance between the equivalent sources and measurement surfaces and for the difference in magnitude between pressure and velocity. Experimental and numerical studies have been conducted to examine the methods. The double layer velocity method seems to be more robust to noise and flanking sound than the combined pressure-velocity method, although it requires an additional measurement surface. On the whole, the separation methods can be useful when the disturbance of the incoming field is significant. Otherwise the direct reconstruction is more accurate and straightforward.

Thresholds for the slope ratio in determining transition time and quantifying diffuser performance in situ.

This study is concerned with an objective measure called the slope ratio that can detect acoustic defects due to unexpected pressure increases such as strong reflections and coincidental constructive interference. The slope ratio is the ratio of the instantaneous slope to the mean slope in a decay curve. The slope ratio was suggested for determining the room acoustic transition time experimentally, but its threshold criteria have not been thoroughly investigated. The thresholds for the slope ratio, particularly for applications such as determining the room acoustic transition time and quantifying in situ diffuseness, are examined for various room impulse responses. For the tested rooms, a slope ratio threshold of 11 gives the most consistent and systematic results.

An acousto-optic beamformer.

There is a great variety of beamforming techniques that can be used for localization of sound sources. The differences among them usually lie in the array layout or in the specific signal processing algorithm used to compute the beamforming output. Any beamforming system consists of a finite number of transducers, which makes beamforming methods vulnerable to spatial aliasing above a certain frequency. The present work uses the acousto-optic effect, i.e., the interaction between sound and light, to localize sound sources in a plane. The use of a beam of light as the sensing element is equivalent to a continuous line aperture with an infinite number of microphones. This makes the proposed acousto-optic beamformer immune to spatial aliasing. This unique feature is illustrated by means of simulations and experimental results within the entire audible frequency range. For ease of comparison, the study is supplemented with measurements carried out with a line array of microphones.

Sound field control with a circular double-layer array of loudspeakers.

This paper describes a method of generating a controlled sound field for listeners inside a circular array of loudspeakers without disturbing people outside the array appreciably. To achieve this objective, a double-layer array of loudspeakers is used. Several solution methods are suggested, and their performance is examined using computer simulations. Two performance indices are used in this work, (a) the level difference between the average sound energy density in the listening zone and that in the quiet zone (sometimes called "the acoustic contrast"), and (b) a normalized measure of the deviations between the desired and the generated sound field in the listening zone. It is concluded that the best compromise is obtained with a method that combines pure contrast maximization with a pressure matching technique.

Sound field reconstruction using acousto-optic tomography.

When sound propagates through a medium, it results in pressure fluctuations that change the instantaneous density of the medium. Under such circumstances, the refractive index that characterizes the propagation of light is not constant, but influenced by the acoustic field. This kind of interaction is known as the acousto-optic effect. The formulation of this physical phenomenon into a mathematical problem can be described in terms of the Radon transform, which makes it possible to reconstruct an arbitrary sound field using tomography. The present work derives the fundamental equations governing the acousto-optic effect in air, and demonstrates that it can be measured with a laser Doppler vibrometer in the audible frequency range. The tomographic reconstruction is tested by means of computer simulations and measurements. The main features observed in the simulations are also recognized in the experimental results. The effectiveness of the tomographic reconstruction is further confirmed with representations of the very same sound field measured with a traditional microphone array.

A note on the modal kurtosis and the concentration factor in reverberation rooms.

The effect known as "weak Anderson localization," "coherent backscattering," or "enhanced back-scattering" is a physical phenomenon that occurs in random systems, e.g., disordered media and linear wave systems, including reverberation rooms: The mean square response is increased at the drive point. In a reverberation room, this means that one can expect an increase of the reverberant sound field at the position of the source that generates the sound field. This affects the sound power output of the source and is therefore of practical concern. The relative increase of reverberant energy is described by the concentration factor, which is usually assumed to be 2. However, because of the stronger direct sound field at the source position, it is obviously very difficult to measure this quantity directly under steady-state conditions. A related parameter of crucial importance for the ensemble statistics of responses in rooms is the modal kurtosis, which is usually assumed to be 3. The modal kurtosis is also very difficult to measure directly. This paper presents the results of an indirect experimental estimation of the two parameters.

Direct formulation of the supersonic acoustic intensity in space domain.

This paper proposes and examines a direct formulation in space domain of the so-called supersonic acoustic intensity. This quantity differs from the usual (active) intensity by excluding the circulating energy in the near-field of the source, providing a map of the acoustic energy that is radiated into the far field. To date, its calculation has been formulated in the wave number domain, filtering out the evanescent waves outside the radiation circle and reconstructing the acoustic field with only the propagating waves. In this study, the supersonic intensity is calculated directly in space domain by means of a two-dimensional convolution between the acoustic field and a spatial filter mask that corresponds to the space domain representation of the radiation circle. Therefore, the acoustic field that propagates effectively to the far field is calculated via direct filtering in space domain. This paper presents the theory, as well as a numerical example to illustrate some fundamental principles. An experimental study on planar radiators was conducted to verify the validity of the technique. The experimental results are presented, and serve to illustrate the usefulness of the analysis, its strengths and limitations.

Beamforming with a circular array of microphones mounted on a rigid sphere (L).

Beamforming with uniform circular microphone arrays can be used for localizing sound sources over 360°. Typically, the array microphones are suspended in free space or they are mounted on a solid cylinder. However, the cylinder is often considered to be infinitely long because the scattering problem has no exact solution for a finite cylinder. Alternatively one can use a solid sphere. This investigation compares the performance of a circular array mounded on a rigid sphere with that of such an array in free space and mounted on an infinite cylinder, using computer simulations. The examined techniques are delay-and-sum and circular harmonics beamforming, and the results are validated experimentally.

Sound field separation with a double layer velocity transducer array (L).

In near-field acoustic holography sound field separation techniques make it possible to distinguish between sound coming from the two sides of the array. This is useful in cases where the sources are not confined to only one side of the array, e.g., in the presence of additional sources or reflections from the other side. This paper examines a separation technique based on measurement of the particle velocity in two closely spaced parallel planes. The purpose of the technique is to recover the particle velocity radiated by a source in the presence of disturbing sound from the opposite side of the array. The technique has been examined and compared with direct velocity based reconstruction, as well as with a technique based on the measurement of the sound pressure and particle velocity. The double layer velocity method circumvents some of the drawbacks of the pressure-velocity based reconstruction, and it can successfully recover the normal velocity radiated by the source, even in the presence of strong disturbing sound.

Extracting the invariant model from the feedback paths of digital hearing aids.

Feedback whistling is a severe problem with hearing aids. A typical acoustical feedback path represents a wave propagation path from the receiver to the microphone and includes many complicated effects among which some are invariant or nearly invariant for all users and in all acoustical environments given a specific type of hearing aids. Based on this observation, a feedback path model that consists of an invariant model and a variant model is proposed. A common-acoustical-pole and zero model-based approach and an iterative least-square search-based approach are used to extract the invariant model from a set of impulse responses of the feedback paths. A hybrid approach combining the two methods is also proposed. The general properties of the three methods are studied using artificial datasets, and the methods are cross-validated using the measured feedback paths. The results show that the proposed hybrid method gives the best overall performance, and the extracted invariant model is effective in modeling the feedback path.

Near field acoustic holography with microphones on a rigid sphere (L).

Spherical near field acoustic holography (spherical NAH) is a technique that makes it possible to reconstruct the sound field inside and just outside a spherical surface on which the sound pressure is measured with an array of microphones. This is potentially very useful for source identification. The sphere can be acoustically transparent or it can be rigid. A rigid sphere is somewhat more practical than an open sphere. However, spherical NAH based on a rigid sphere is only valid if it can be assumed that the sphere has a negligible influence on the incident sound field, and this is not necessarily a good assumption when the sphere is very close to a radiating surface. This Letter examines the matter through simulations and experiments.

Smearing technique for vibration analysis of simply supported cross-stiffened and doubly curved thin rectangular shells.

Plates stiffened with ribs can be modeled as equivalent homogeneous isotropic or orthotropic plates. Modeling such an equivalent smeared plate numerically, say, with the finite element method requires far less computer resources than modeling the complete stiffened plate. This may be important when a number of stiffened plates are combined in a complicated assembly composed of many plate panels. However, whereas the equivalent smeared plate technique is well established and recently improved for flat panels, there is no similar established technique for doubly curved stiffened shells. In this paper the improved smeared plate technique is combined with the equation of motion for a doubly curved thin rectangular shell, and a solution is offered for using the smearing technique for stiffened shell structures. The developed prediction technique is validated by comparing natural frequencies and mode shapes as well as forced responses from simulations based on the smeared theory with results from experiments with a doubly curved cross-stiffened shell. Moreover, natural frequencies of cross-stiffened panels determined by finite element simulations that include the exact cross-sectional geometries of panels with cross-stiffeners are compared with predictions based on the smeared theory for a range of different panel curvatures. Good agreement is found.

Ensemble statistics of active and reactive sound intensity in reverberation rooms.

This paper examines fundamental statistical properties of the active and reactive sound intensity in reverberant enclosures driven with pure tones. The existing theory for sound intensity in a diffuse sound field, which is based on Waterhouse's random wave model and therefore limited to the region of high modal overlap, is extended to the region of low modal overlap by taking account of the random fluctuations of the sound power emitted by the source that generates the sound field. The validity of the extended model is confirmed by experimental and numerical results.

Room acoustic transition time based on reflection overlap.

A transition time is defined based on the temporal overlap of reflected pulses in room impulse responses. Assuming specular reflections only, the temporal distance between adjacent reflections, which is proportional to the volume of a room, is compared with the characteristic width of a pulse at time t, which is mainly controlled by the absorption characteristics of the boundary surfaces of the room. Scattering, diffuse reflections, and diffraction, which facilitate the overlapping process, have not been taken into account. Measured impulse responses show that the transition occurs earlier in a room with nonuniform absorption and furniture than in a room that satisfies the underlying assumptions.

Effort variation regularization in sound field reproduction.

In this paper, active control is used in order to reproduce a given sound field in an extended spatial region. A method is proposed which minimizes the reproduction error at a number of control positions with the reproduction sources holding a certain relation within their complex strengths. Specifically, it is suggested that the phase differential of the source driving signals should be in agreement with the phase differential of the desired sound pressure field. The performance of the suggested method is compared with that of conventional effort regularization, wave field synthesis (WFS), and adaptive wave field synthesis (AWFS), both under free-field conditions and in reverberant rooms. It is shown that effort variation regularization overcomes the problems associated with small spaces and with a low ratio of direct to reverberant energy, improving thus the reproduction accuracy in the listening room.