On the selection of the number of beamformers in beamforming-based binaural reproduction.

In recent years, spatial audio reproduction has been widely researched with many studies focusing on headphone-based spatial reproduction. A popular format for spatial audio is higher order Ambisonics (HOA), where a spherical microphone array is typically used to obtain the HOA signals. When a spherical array is not available, beamforming-based binaural reproduction (BFBR) can be used, where signals are captured with arrays of a general configuration. While shown to be useful, no comprehensive studies of BFBR have been presented and so its limitations and other design aspects are not well understood. This paper takes an initial step towards developing a theory for BFBR and develops guidelines for selecting the number of beamformers. In particular, the average directivity factor of the microphone array is proposed as a measure for supporting this selection. The effect of head-related transfer function (HRTF) order truncation that occurs when using too many beamformer directions is presented and studied. In addition, the relation between HOA-based binaural reproduction and BFBR is discussed through analysis based on a spherical array. A simulation study is then presented, based on both a spherical and a planar array, demonstrating the proposed guidelines. A listening test verifies the perceptual attributes of the methods presented in this study. These results can be used for more informed beamformer design for BFBR.

Modal smoothing for analysis of room reflections measured with spherical microphone and loudspeaker arrays.

Spatial analysis of room acoustics is an ongoing research topic. Microphone arrays have been employed for spatial analyses with an important objective being the estimation of the direction-of-arrival (DOA) of direct sound and early room reflections using room impulse responses (RIRs). An optimal method for DOA estimation is the multiple signal classification algorithm. When RIRs are considered, this method typically fails due to the correlation of room reflections, which leads to rank deficiency of the cross-spectrum matrix. Preprocessing methods for rank restoration, which may involve averaging over frequency, for example, have been proposed exclusively for spherical arrays. However, these methods fail in the case of reflections with equal time delays, which may arise in practice and could be of interest. In this paper, a method is proposed for systems that combine a spherical microphone array and a spherical loudspeaker array, referred to as multiple-input multiple-output systems. This method, referred to as modal smoothing, exploits the additional spatial diversity for rank restoration and succeeds where previous methods fail, as demonstrated in a simulation study. Finally, combining modal smoothing with a preprocessing method is proposed in order to increase the number of DOAs that can be estimated using low-order spherical loudspeaker arrays.

Spectral equalization in binaural signals represented by order-truncated spherical harmonics.

The synthesis of binaural signals from spherical microphone array recordings has been recently proposed. The limited spatial resolution of the reproduced signal due to order-limited reproduction has been previously investigated perceptually, showing spatial perception ramifications, such as poor source localization and limited externalization. Furthermore, this spatial order limitation also has a detrimental effect on the frequency content of the signal and its perceived timbre, due to the rapid roll-off at high frequencies. In this paper, the underlying causes of this spectral roll-off are described mathematically and investigated numerically. A digital filter that equalizes the frequency spectrum of a low spatial order signal is introduced and evaluated. A comprehensive listening test was conducted to study the influence of the filter on the perception of the reproduced sound. Results indicate that the suggested filter is beneficial for restoring the timbral composition of order-truncated binaural signals, while conserving, and even improving, some spatial properties of the signal.

Design framework for spherical microphone and loudspeaker arrays in a multiple-input multiple-output system.

Spherical microphone arrays (SMAs) and spherical loudspeaker arrays (SLAs) facilitate the study of room acoustics due to the three-dimensional analysis they provide. More recently, systems that combine both arrays, referred to as multiple-input multiple-output (MIMO) systems, have been proposed due to the added spatial diversity they facilitate. The literature provides frameworks for designing SMAs and SLAs separately, including error analysis from which the operating frequency range (OFR) of an array is defined. However, such a framework does not exist for the joint design of a SMA and a SLA that comprise a MIMO system. This paper develops a design framework for MIMO systems based on a model that addresses errors and highlights the importance of a matched design. Expanding on a free-field assumption, errors are incorporated separately for each array and error bounds are defined, facilitating error analysis for the system. The dependency of the error bounds on the SLA and SMA parameters is studied and it is recommended that parameters should be chosen to assure matched OFRs of the arrays in MIMO system design. A design example is provided, demonstrating the superiority of a matched system over an unmatched system in the synthesis of directional room impulse responses.

Theory and investigation of acoustic multiple-input multiple-output systems based on spherical arrays in a room.

Spatial attributes of room acoustics have been widely studied using microphone and loudspeaker arrays. However, systems that combine both arrays, referred to as multiple-input multiple-output (MIMO) systems, have only been studied to a limited degree in this context. These systems can potentially provide a powerful tool for room acoustics analysis due to the ability to simultaneously control both arrays. This paper offers a theoretical framework for the spatial analysis of enclosed sound fields using a MIMO system comprising spherical loudspeaker and microphone arrays. A system transfer function is formulated in matrix form for free-field conditions, and its properties are studied using tools from linear algebra. The system is shown to have unit-rank, regardless of the array types, and its singular vectors are related to the directions of arrival and radiation at the microphone and loudspeaker arrays, respectively. The formulation is then generalized to apply to rooms, using an image source method. In this case, the rank of the system is related to the number of significant reflections. The paper ends with simulation studies, which support the developed theory, and with an extensive reflection analysis of a room impulse response, using the platform of a MIMO system.

Spherical array processing for acoustic analysis using room impulse responses and time-domain smoothing.

Room impulse responses (RIRs) have been widely used for room acoustics analysis. One of the major objectives in room acoustics analysis is characterizing the directions of arrival (DOA) of the direct sound and early room reflections. In the past, spherical microphone arrays have been used to sample the sound field, taking advantage of their spatial symmetry, and various optimal array processing methods have been suggested for DOA estimation. However, these methods fail when the sound field is composed of highly correlated components, such as room reflections, since the cross-spectrum matrix may be of deficient rank. Recently, a preprocessing method incorporating smoothing of the cross-correlation matrix in the frequency domain has been suggested to overcome the rank deficiency. However, when using low-order spherical arrays, this method also fails due to the need to estimate the DOA of a group of reflections simultaneously. In this paper, an alternative time-domain smoothing approach is suggested. The method utilizes the time behavior of the RIR to separate early reflections, together with representation of the signal in the spherical-harmonics domain, to achieve improved performance over current methods. Simulation and experimental studies illustrate the limitations of the former method and the advantages of the suggested method.

Spatial perception of sound fields recorded by spherical microphone arrays with varying spatial resolution.

The area of sound field synthesis has significantly advanced in the past decade, facilitated by the development of high-quality sound-field capturing and re-synthesis systems. Spherical microphone arrays are among the most recently developed systems for sound field capturing, enabling processing and analysis of three-dimensional sound fields in the spherical harmonics domain. In spite of these developments, a clear relation between sound fields recorded by spherical microphone arrays and their perception with a re-synthesis system has not yet been established, although some relation to scalar measures of spatial perception was recently presented. This paper presents an experimental study of spatial sound perception with the use of a spherical microphone array for sound recording and headphone-based binaural sound synthesis. Sound field analysis and processing is performed in the spherical harmonics domain with the use of head-related transfer functions and simulated enclosed sound fields. The effect of several factors, such as spherical harmonics order, frequency bandwidth, and spatial sampling, are investigated by applying the repertory grid technique to the results of the experiment, forming a clearer relation between sound-field capture with a spherical microphone array and its perception using binaural synthesis regarding space, frequency, and additional artifacts. The experimental study clearly shows that a source will be perceived more spatially sharp and more externalized when represented by a binaural stimuli reconstructed with a higher spherical harmonics order. This effect is apparent from low spherical harmonics orders. Spatial aliasing, as a result of sound field capturing with a finite number of microphones, introduces unpleasant artifacts which increased with the degree of aliasing error.

Objective performance analysis of spherical microphone arrays for speech enhancement in rooms.

Reverberation and noise have a significant effect on the intelligibility of speech in rooms. The detection of clear speech in highly reverberant and noisy enclosures is an extremely difficult task. Recently, spherical microphone arrays have been studied for processing of sound fields in three-dimensions, with applications ranging from acoustic analysis to speech enhancement. This paper presents the derivation of a model that facilitates the prediction of spherical array configurations that guarantee an acceptable level of speech intelligibility in reverberant and noisy environments. A spherical microphone array is employed to generate a spatial filter that maximizes speech intelligibility according to an objective measure that combines the effects of both reverberation and noise. The spherical array beamformer is designed to enhance the speech signal while minimizing noise power and maintaining robustness over a wide frequency range. The paper includes simulation and experimental studies with a comparison to speech transmission index based analysis to provide initial validation of the model. Examples are presented in which the minimum number of microphones in a spherical array can be determined from environment conditions such as reverberation time, noise level, and distance of the array to the speech source.

Acoustic analysis by spherical microphone array processing of room impulse responses.

Spherical microphone arrays have been recently used for room acoustics analysis, to detect the direction-of-arrival of early room reflections, and compute directional room impulse responses and other spatial room acoustics parameters. Previous works presented methods for room acoustics analysis using spherical arrays that are based on beamforming, e.g., delay-and-sum, regular beamforming, and Dolph-Chebyshev beamforming. Although beamforming methods provide useful directional selectivity, optimal array processing methods can provide enhanced performance. However, these algorithms require an array cross-spectrum matrix with a full rank, while array data based on room impulse responses may not satisfy this condition due to the single frame data. This paper presents a smoothing technique for the cross-spectrum matrix in the frequency domain, designed for spherical microphone arrays, that can solve the problem of low rank when using room impulse response data, therefore facilitating the use of optimal array processing methods. Frequency smoothing is shown to be performed effectively using spherical arrays, due to the decoupling of frequency and angular components in the spherical harmonics domain. Experimental study with data measured in a real auditorium illustrates the performance of optimal array processing methods such as MUSIC and MVDR compared to beamforming.

Investigation of spherical loudspeaker arrays for local active control of sound.

Active control of sound can be employed globally to reduce noise levels in an entire enclosure, or locally around a listener's head. Recently, spherical loudspeaker arrays have been studied as multiple-channel sources for local active control of sound, presenting the fundamental theory and several active control configurations. In this paper, important aspects of using a spherical loudspeaker array for local active control of sound are further investigated. First, the feasibility of creating sphere-shaped quiet zones away from the source is studied both theoretically and numerically, showing that these quiet zones are associated with sound amplification and poor system robustness. To mitigate the latter, the design of shell-shaped quiet zones around the source is investigated. A combination of two spherical sources is then studied with the aim of enlarging the quiet zone. The two sources are employed to generate quiet zones that surround a rigid sphere, investigating the application of active control around a listener's head. A significant improvement in performance is demonstrated in this case over a conventional headrest-type system that uses two monopole secondary sources. Finally, several simulations are presented to support the theoretical work and to demonstrate the performance and limitations of the system.

Acoustic centering of sources measured by surrounding spherical microphone arrays.

The radiation patterns of acoustic sources have great significance in a wide range of applications, such as measuring the directivity of loudspeakers and investigating the radiation of musical instruments for auralization. Recently, surrounding spherical microphone arrays have been studied for sound field analysis, facilitating measurement of the pressure around a sphere and the computation of the spherical harmonics spectrum of the sound source. However, the sound radiation pattern may be affected by the location of the source inside the microphone array, which is an undesirable property when aiming to characterize source radiation in a unique manner. This paper presents a theoretical analysis of the spherical harmonics spectrum of spatially translated sources and defines four measures for the misalignment of the acoustic center of a radiating source. Optimization is used to promote optimal alignment based on the proposed measures and the errors caused by numerical and array-order limitations are investigated. This methodology is examined using both simulated and experimental data in order to investigate the performance and limitations of the different alignment methods.

Room volume classification from room impulse response using statistical pattern recognition and feature selection.

Classification of the room volume from the room impulse response (RIR) can be useful in acoustic scene analysis applications, using RIR that is provided directly, or estimated from audio recordings. Current methods for estimating the room volume from the RIR require the source-to-receiver distance, and may be sensitive to differences in absorption. A room volume classification method is presented that does not require the source-to-receiver distance, and which is potentially robust to differences in absorption. Room volume features are defined that are related to the room volume and may be extracted from the RIR. Gaussian mixture models are trained to model room volume classes. Room volume is classified according to a maximum likelihood criterion that is normalized with a background model. Feature selection is performed with different classification error criteria. Both simulated and measured RIRs were examined, achieving an equal error rate of 0.1% and 19.1%, respectively.

Interaural cross correlation in a sound field represented by spherical harmonics.

Spatial impression is an important acoustic quality of concert halls. An accepted objective measure for spatial impression is the interaural cross-correlation (IACC) coefficient. Recently, spherical microphone arrays have been studied for room acoustics analysis and music recordings. This study presents a theoretical formulation for the computation of IACC using spherical-harmonics representations of the sound field, as measured by spherical microphone arrays, and spherical-harmonics representation of head-related transfer functions (HRTFs), taken from HRTF databases. As spherical microphone arrays typically use a finite number of microphones, they may not be able to capture the complete spatial information in a sound field. Therefore, the effect of limited spherical-harmonics order on the accuracy of IACC approximation using the proposed method is studied using simulated and measured data. The method presented in this paper can be further used to study the effect of limited spatial information on the spatial perception of sound fields.

Spherical loudspeaker array for local active control of sound.

Active control of sound has been employed to reduce noise levels around listeners' head using destructive interference from noise-canceling sound sources. Recently, spherical loudspeaker arrays have been studied as multiple-channel sound sources, capable of generating sound fields with high complexity. In this paper, the potential use of a spherical loudspeaker array for local active control of sound is investigated. A theoretical analysis of the primary and secondary sound fields around a spherical sound source reveals that the natural quiet zones for the spherical source have a shell-shape. Using numerical optimization, quiet zones with other shapes are designed, showing potential for quiet zones with extents that are significantly larger than the well-known limit of a tenth of a wavelength for monopole sources. The paper presents several simulation examples showing quiet zones in various configurations.

High-resolution plane-wave decomposition in an auditorium using a dual-radius scanning spherical microphone array.

The spatial and temporal distribution of early reflections in an auditorium is considered important for sound perception. Previous studies presented measurement and analysis methods based on spherical microphone arrays and plane-wave decomposition that could provide information on the direction and time of arrival of early reflections. This paper presents recent results of room acoustics analysis based on a spherical microphone array, which employs high spherical harmonics order for improved spatial resolution, and a dual-radius spherical measurement array to avoid ill-conditioning at the null frequencies of the spherical Bessel function. Spatial-temporal analysis is performed to produce directional impulse responses, while analysis based on the windowed Fourier transform is employed to detect direction of arrival of individual reflections at selected frequencies. Experimental results of sound-field analysis in a real auditorium are also presented.

Experimental investigation of spatial correlation in broadband reverberant sound fields.

The spatial correlation has previously been investigated for tonal and narrow-band sound fields. This letter presents an experimental investigation of the spatial correlation coefficients in a reverberation chamber driven by broadband signals. The main objective is to verify recent theoretical results for broadband spatial correlation in diffuse sound fields. Experimental results show good agreement with theoretical predictions when the frequency band of the sound field is entirely above the Schroeder frequency.

Sweet spot size of virtual acoustic imaging systems at asymmetric listener locations.

Virtual acoustic imaging systems are effective when the listener's head location is close to the head location assumed when the system was designed. The "sweet spot" refers to the spatial bubble of head location in which the system is still effective. Some of the previous work investigating the "stereo dipole" acoustic imaging system shows that for the traditional on-axis listener location the "sweet spot" is about +/-5 cm for lateral head translations. Larger head movements than this require an update of the virtual acoustic imaging filters. The interest here is the "sweet spot" size at off-axis asymmetric listener locations or an understanding of how often one needs to update the filters to ensure the listener perceives a stable virtual image as they move. The examination of the off-axis "sweet spot" size comprises a theoretical acoustic analysis, computer simulations, and a subjective study. The simulations and subjective evaluation both demonstrate that the width of tolerable lateral head translations is comparable for the symmetric on-axis listener location and asymmetric listener locations that are as far as 25 cm off-axis.

Novel active noise-reducing headset using earshell vibration control.

Active noise-reducing (ANR) headsets are available commercially in applications varying from aviation communication to consumer audio. Current ANR systems use passive attenuation at high frequencies and loudspeaker-based active noise control at low frequencies to achieve broadband noise reduction. This paper presents a novel ANR headset in which the external noise transmitted to the user's ear via earshell vibration is reduced by controlling the vibration of the earshell using force actuators acting against an inertial mass or the earshell headband. Model-based theoretical analysis using velocity feedback control showed that current piezoelectric actuators provide sufficient force but require lower stiffness for improved low-frequency performance. Control simulations based on experimental data from a laboratory headset showed that good performance can potentially be achieved in practice by a robust feedback controller, while a single-frequency real-time control experiment verified that noise reduction can be achieved using earshell vibration control.

Combined feedback-feedforward active noise-reducing headset--the effect of the acoustics on broadband performance.

Active noise-reducing headsets that employ analog feedback control and provide good broadband attenuation are commercially available for a wide range of applications. Recent studies have explored the integration of an adaptive digital feedforward controller with the analog feedback controller to provide additional attenuation of periodic noise components. This paper presents an experimental study of such a combined control system, but with both feedback- and feedforward controllers attenuating broadband noise. Good performance is demonstrated in a reverberant sound field, while under direct sound-field conditions the attenuation performance of the feedforward controller is shown to be dependent on head position. The paper concludes with an analysis of the forward path delay showing how the passive attenuation mechanism improves broadband performance.