A time-domain nearfield beamformer with spherical harmonic decomposition.

This paper proposes a time-domain nearfield beamformer with spherical harmonic decomposition. The beamformer design is separated into two stages: sound field measurement and beamformer coefficient design. This makes it easier for the beamformer to be implemented by different array structures. The beamformer coefficients are further separated into several parts, making it easier to design a beamformer with different characteristics. The time-domain implementation minimizes the latency between the array input and the beamformer response, and the nearfield focusing improves the farfield noise suppression ability of the beamformer. The proposed beamformer could be useful for emerging acoustic applications such as virtual reality and drones, and for further development of more advanced real-time nearfield beamformers. Simulations and experiments examine the performance of the proposed beamformer.

Time-frequency-dependent directional analysis of room reflections using eigenbeam processing and von Mises-Fisher clustering.

The knowledge of frequency-dependent spatiotemporal features of the reflected soundfield is essential in optimizing the perception quality of spatial audio applications. For this purpose, we need a reliable room acoustic analyzer that can conceive the spatial variations in a decaying reflected soundfield according to the frequency-dependent surface properties and source directivity. This paper introduces a time-frequency-dependent angular reflection power distribution model represented by a von Mises-Fisher (vMF) mixture function to facilitate manifold analysis of a reverberant soundfield. The proposed approach utilizes the spatial correlation of higher-order eigenbeams to deduce the directional reflection power vectors, which are then synthesized into a vMF mixture model. The experimental study demonstrates the directional power variations of early reflections and late reverberations across different frequencies. This work also introduces a measure called the directivity time-span to quantify the duration of anisotropic reflections before it decays into a totally diffused field. We validate the subband performance by comparing it with the eigenbeam multiple signal classification method. The results prove the influence of source position, source directivity, and room environment in the distribution of reflection power, whereas the directivity time-span behaves independent of the source positions.

Secondary channel estimation in spatial active noise control systems using a single moving higher order microphone.

Spatial active noise control (ANC) systems focus on minimizing unwanted acoustic noise over continuous spatial regions by generating anti-noise fields with secondary loudspeakers. Conventionally, error microphones are necessary inside the region to measure the channels from the secondary loudspeakers to the error microphones and record the residual sound field during the noise control. These error microphones highly limit the implementation of spatial ANC systems because of their impractical geometry and obstruction to the users from accessing the region. Recent advances, such as virtual sensing, focus on ANC with microphones placed away from the region. While these techniques relax the usage of error microphones during the noise control, an error microphone array remains necessary during the secondary channel estimation. In this paper, we propose a method to estimate secondary channels without using an error microphone array. Instead, a moving higher order microphone is applied to obtain the secondary channels from the secondary loudspeakers to the region of interest, which includes all desired error microphone locations. By simulation, we show that the proposed method is robust against various measuring errors introduced by the movement of the microphone and is suitable for the secondary channel estimation in spatial ANC systems.

2.5D multizone reproduction using weighted mode matching: Performance analysis and experimental validation.

Mode-matching based multizone reproduction has been mainly focused on a purely two-dimensional (2D) theory, where infinite-long 2D secondary sources are assumed for 2D multizone reproduction. Its extension to the three-dimensional (3D) case requires more secondary sources and a higher computational complexity. This work investigates a more practical setup to use 3D sound sources as secondary sources for multizone reproduction in a 2D horizontal plane, i.e., 2.5D multizone reproduction. A weighted mode-matching approach is proposed to solve the dimensionality mismatch between the 2D desired sound field and 3D reproduced sound field. The weighting is based on an integral of Bessel-spherical harmonic modes over the entire control region. A detailed analysis of the weighting function is provided to show that the proposed method controls all the reproduction modes present on the 2D plane to minimize the reproduction error. The method is validated in both simulation-based and hardware-based experiments. The results demonstrate that in comparison with the conventional sectorial mode-matching method, the proposed approach can achieve more accurate reproduction over a wide frequency range and a large control region.

Coherence-based performance analysis on noise reduction in multichannel active noise control systems.

Active noise control (ANC) over an extended spatial region using multiple microphones and multiple loudspeakers has become an important problem. The maximum noise reduction (NR) potential over the control area is a critical evaluation variable as it indicates the fundamental limitation of a given ANC system. In this paper, a method to mathematically formulate the NR potential for any given multichannel ANC systems is developed. First, the residual error in the multichannel feedforward ANC system is formulated, and then the multiple-input-multiple-output problem is decomposed into the parallel-channel problem. The total energy of the residual error is further decomposed into three different terms representing (i) the signal coherence between the reference signals and error signals, (ii) the filter, and (iii) the system null space. The experimental results validate the proposed evaluation method and illustrate the effectiveness on the maximum NR performance evaluation for given systems. Using the proposed analyzing method, more insight into the contribution of each component to the NR potential can be achieved.

Real-time separation of non-stationary sound fields on spheres.

The sound field separation methods can separate the target field from the interfering noises, facilitating the study of the acoustic characteristics of the target source, which is placed in a noisy environment. However, most of the existing sound field separation methods are derived in the frequency-domain, thus they are best suited for separating stationary sound fields. In this paper, a time-domain sound field separation method is developed that can separate the non-stationary sound field generated by the target source over a sphere in real-time. A spherical array sets up a boundary between the target source and the interfering sources, such that the outgoing field on the array is only generated by the target source. The proposed method decomposes the pressure and the radial particle velocity measured by the array into spherical harmonic coefficients, and recovers the target outgoing field based on the time-domain relationship between the decomposition coefficients and the theoretically derived spatial filter responses. Simulations show the proposed method can separate non-stationary sound fields both in free field and room environments, and over a longer duration with small errors. The proposed method could serve as a foundation for developing future time-domain spatial sound field manipulation algorithms.

Spatial sound intensity vectors in spherical harmonic domain.

Sound intensity is a fundamental quantity describing acoustic wave fields and it contains both energy and directivity information. It is used in a variety of applications such as source localization, reproduction, and power measurement. Until now, intensity is defined at a point in space, however given sound propagates over space, knowing its spatial distribution could be more powerful. This paper formulates spatial sound intensity vectors in spherical harmonic domain such that the vectors contain energy and directivity information over continuous spatial regions. These representations are derived with finite sets of closed form coefficients enabling ease of implementation.

Parameterization of the binaural room transfer function using modal decomposition.

Binaural room responses are normally measured on a listening subject in a room. The measurements, however, rapidly change with the source and receiver position. In addition, the measurements taken in a room can only be used to simulate scenes of that environment. In this work, an efficient parameterization of the binaural room transfer function is proposed, which has separable representations for the direct-path component and the reverberation component, thus providing a flexible way to generate binaural room responses for different environments and listeners. In addition, this parameterization uses wave equation solutions as basis functions and is continuous in space.

Active control of outgoing noise fields in rooms.

Current active noise control systems can cancel noises in a duct effectively. However, they are insufficient for suppressing complex noise fields in time-varying rooms. This paper develops an active noise control system that can cancel tonal noise fields produced by a primary source in a room. The problem of tonal noise field control is formulated as estimating and canceling the outgoing field on a sphere surrounding the primary source. The proposed system limits the energy of the primary source radiating out of the sphere, thereby creating a global quiet zone inside the room. In addition, it removes the need for online secondary path estimation with reduced influence on desired sound fields in the room. A method for estimating the outgoing field on a sphere is presented, together with a wave-domain algorithm for controlling the outgoing field. Simulations and hardware demonstrations show the proposed system can reduce tonal noise fields in a room and over a wide frequency range.

Spherical harmonics based generalized image source method for simulating room acoustics.

Allen and Berkley's image source method (ISM) is proven to be a very useful and popular technique for simulating the acoustic room transfer function (RTF) in reverberant rooms. It is based on the assumption that the source and receiver of interest are both omnidirectional. With the inherent directional nature of practical loudspeakers and the increasing use of directional microphones, the above assumption is often invalid. The main objective of this paper is to generalize the frequency domain ISM in the spherical harmonics domain such that it could simulate the RTF between practical transducers with higher-order directivity. This is achieved by decomposing transducer directivity patterns in terms of spherical harmonics and by applying the concept of image sources in spherical harmonics based propagation patterns. Therefore, from now on, any transducer can be modeled in the spherical harmonics domain with a realistic directivity pattern and incorporated with the proposed method to simulate room acoustics more accurately. We show that the proposed generalization also has an alternate use in terms of enabling RTF simulations for moving point-transducers inside pre-defined source and receiver regions.

Acoustic reciprocity: An extension to spherical harmonics domain.

Acoustic reciprocity is a fundamental property of acoustic wavefields that is commonly used to simplify the measurement process of many practical applications. Traditionally, the reciprocity theorem is defined between a monopole point source and a point receiver. Intuitively, it must apply to more complex transducers than monopoles. In this paper, the authors formulate the acoustic reciprocity theory in the spherical harmonics domain for directional sources and directional receivers with higher order directivity patterns.

Analysis and control of multi-zone sound field reproduction using modal-domain approach.

Multi-zone sound control aims to reproduce multiple sound fields independently and simultaneously over different spatial regions within the same space. This paper investigates the multi-zone sound control problem formulated in the modal domain using the Lagrange cost function and provides a modal-domain analysis of the problem. The Lagrange cost function is formulated to represent a quadratic objective of reproducing a desired sound field within the bright zone and with constraints on sound energy in the dark zone and global region. A fundamental problem in multi-zone reproduction is interzone sound interference, where based on the geometry of the sound zones and the desired sound field within the bright zone the achievable reproduction performance is limited. The modal-domain Lagrangian solution demonstrates the intrinsic ill-posedness of the problem, based on which a parameter, the coefficient of realisability, is developed to evaluate the reproduction limitation. The proposed reproduction method is based on controlling the interference between sound zones and sound leakage outside the sound zones, resulting in a suitable compromise between good bright zone performance and satisfactory dark zone performance. The performance of the proposed design is demonstrated through numerical simulations of two-zone reproduction in free-field and in reverberant environments.

Multichannel active noise control for spatially sparse noise fields.

Multi-channel active noise control (ANC) is currently an attractive solution for the attenuation of low-frequency noise fields, in three-dimensional space. This paper develops a controller for the case when the noise source components are sparsely distributed in space. The anti-noise signals are designed as in conventional ANC to minimize the residual errors but with an additional term containing an ℓl norm regularization applied to the signal magnitude. This results in that only secondary sources close to the noise sources are required to be active for cancellation of sparse noise fields. Adaptive algorithms with low computational complexity and faster convergence speeds are proposed.

Parameterization of the three-dimensional room transfer function in horizontal plane.

This letter proposes an efficient parameterization of the three-dimensional room transfer function (RTF) which is robust for the position variations of source and receiver in respective horizontal planes. Based on azimuth harmonic analysis, the proposed method exploits the underlying properties of the associated Legendre functions to remove a portion of the spherical harmonic coefficients of RTF which have no contribution in the horizontal plane. This reduction leads to a flexible measuring-point structure consisting of practical concentric circular arrays to extract horizontal plane RTF coefficients. The accuracy of the above parameterization is verified through numerical simulations.

Theory and design of compact hybrid microphone arrays on two-dimensional planes for three-dimensional soundfield analysis.

Soundfield analysis based on spherical harmonic decomposition has been widely used in various applications; however, a drawback is the three-dimensional geometry of the microphone arrays. In this paper, a method to design two-dimensional planar microphone arrays that are capable of capturing three-dimensional (3D) spatial soundfields is proposed. Through the utilization of both omni-directional and first order microphones, the proposed microphone array is capable of measuring soundfield components that are undetectable to conventional planar omni-directional microphone arrays, thus providing the same functionality as 3D arrays designed for the same purpose. Simulations show that the accuracy of the planar microphone array is comparable to traditional spherical microphone arrays. Due to its compact shape, the proposed microphone array greatly increases the feasibility of 3D soundfield analysis techniques in real-world applications.

Comparison of sound reproduction using higher order loudspeakers and equivalent line arrays in free-field conditions.

Higher order sound sources of Nth order can radiate sound with 2N + 1 orthogonal radiation patterns, which can be represented as phase modes or, equivalently, amplitude modes. This paper shows that each phase mode response produces a spiral wave front with a different spiral rate, and therefore a different direction of arrival of sound. Hence, for a given receiver position a higher order source is equivalent to a linear array of 2N + 1 monopole sources. This interpretation suggests performance similar to a circular array of higher order sources can be produced by an array of sources, each of which consists of a line array having monopoles at the apparent source locations of the corresponding phase modes. Simulations of higher order arrays and arrays of equivalent line sources are presented. It is shown that the interior fields produced by the two arrays are essentially the same, but that the exterior fields differ because the higher order sources produces different equivalent source locations for field positions outside the array. This work provides an explanation of the fact that an array of L Nth order sources can reproduce sound fields whose accuracy approaches the performance of (2N + 1)L monopoles.

Binaural sound source localization using the frequency diversity of the head-related transfer function.

The spectral localization cues contained in the head-related transfer function are known to play a contributory role in the sound source localization abilities of humans. However, existing localization techniques are unable to fully exploit this diversity to accurately localize a sound source. The availability of just two measured signals complicates matters further, and results in front to back confusions and poor performance distinguishing between the source locations in a vertical plane. This study evaluates the performance of a source location estimator that retains the frequency domain diversity of the head-related transfer function. First, a method for extracting the directional information in the subbands of a broadband signal is described, and a composite estimator based on signal subspace decomposition is introduced. The localization performance is experimentally evaluated for single and multiple source scenarios in the horizontal and vertical planes. The proposed estimator's ability to successfully localize a sound source and resolve the ambiguities in the vertical plane is demonstrated, and the impact of the source location, knowledge of the source and the effect of reverberation is discussed.

Frequency-radial duality based photoacoustic image reconstruction.

Photoacoustic image reconstruction algorithms are usually slow due to the large sizes of data that are processed. This paper proposes a method for exact photoacoustic reconstruction for the spherical geometry in the limiting case of a continuous aperture and infinite measurement bandwidth that is faster than existing methods namely (1) backprojection method and (2) the Norton-Linzer method [S. J. Norton and M. Linzer, "Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solution for plane, cylindrical and spherical apertures," Biomedical Engineering, IEEE Trans. BME 28, 202-220 (1981)]. The initial pressure distribution is expanded using a spherical Fourier Bessel series. The proposed method estimates the Fourier Bessel coefficients and subsequently recovers the pressure distribution. A concept of frequency-radial duality is introduced that separates the information from the different radial basis functions by using frequencies corresponding to the Bessel zeros. This approach provides a means to analyze the information obtained given a measurement bandwidth. Using order analysis and numerical experiments, the proposed method is shown to be faster than both the backprojection and the Norton-Linzer methods. Further, the reconstructed images using the proposed methodology were of similar quality to the Norton-Linzer method and were better than the approximate backprojection method.

Higher order differential-integral microphone arrays.

This paper develops theory to design higher order directional microphone arrays. The proposed higher order designs have similar inter sensor spacings as traditional first and second order differential arrays. The Jacobi-Anger expansion is used to exploit the underlying structure of microphone signals from pairs of closely spaced sensors. Specifically, the difference and sum of these microphone signals are processed to design the novel directional array.