Hai Morgenstern

Joint spherical beam forming for directional analysis of reflections in rooms

This contribution presents a new approach for analyzing spatial directions in room impulse responses captured with source and receiver of adjustable directivity. A distinct peak in a room impulse response is usually associated with an acoustic path length of direct or reflected sound. Given the ability to modify the directivity of source and receiver by spherical beamforming, beam coefficients can be adjusted as to emphasize the peak at a preselected time instant. We present a new approach to jointly optimize the coefficients for both source and receiver under the constraint of a unit peak amplitude while minimizing the energy of the response. The beam pattern described by these coefficients highlights the dominant acoustic path directions of the corresponding path length at the source and the receiver.

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.

Enhanced spatial analysis of room acoustics using acoustic multiple-input multiple-output (MIMO) systems

Standard acoustic measurements in enclosures typically employ single-input single-output (SISO) acoustic systems. The parameters obtained from these measurements describe features of energy decay and do not characterize spatial attributes of the enclosure. Directional analysis of enclosures became popular with the introduction of microphone and loudspeaker arrays. In particular, spherical arrays have been shown to be highly beneficial for spatial analysis. Spherical microphone arrays facilitate the estimation of the arrival direction of the direct and reflected sound, while the use of both loudspeaker and microphones arrays can support the estimation of both radiation and arrival directions, with the application of conventional beamforming methods. However, when several reflections are attributed to the same time bin in a discrete impulse response, reflection paths may not be uniquely determined by existing beamforming techniques. We present a new method to uniquely determine source and receiver direction...

Analysis of acoustic MIMO systems in enclosed sound fields

Methods for room acoustic analysis based on a single loudspeaker and a single microphone have been extensively studied, both theoretically and experimentally. Although measurement techniques for acquiring and processing spatial information in a room using arrays of loudspeakers and microphones have been recently proposed, the current literature in room acoustics does not describe the use of multiple-input multiple-output (MIMO) systems in a comprehensive manner. The aim of this paper is, therefore, to present an initial theoretical framework for the spatial analysis of enclosed sound fields using an acoustic MIMO system, based on a spherical loudspeaker array and a spherical microphone array. The fundamental characteristics of the system transfer matrix are shown to be invariant to rotation of the arrays, with its rank dependant on the number of reflections in the room. The paper concludes with a simulation study validating the theoretical models.

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.

Spatial analysis of sound fields in rooms using spherical MIMO systems

The perception of sound by human listeners in a room has been shown to be affected by the spatial attributes of the sound field. These spatial attributes have been studied using microphone and loudspeaker arrays separately. Systems that combine both loudspeaker and microphone arrays, termed multiple-input multiple-output (MIMO) systems, facilitate enhanced spatial analysis compared to systems with a single array, thanks to the simultaneous use of the arrays and the additional spatial diversity. Using MIMO systems, room impulse responses (RIRs) can be presented using matrix notation, which enables a unique study of a sound field’s spatial attributes, employing methods from linear algebra. For example, a matrix’s rank and null space can be studied to reveal spatial information on a room, such as the number of dominant room reflections and their direction of arrival to the microphone array and the direction of radiation from the loudspeaker array. In this contribution, a theory of the spatial analysis of a sound field using a MIMO system comprised of spherical arrays is developed and a simulation study is presented. In the study, tools proposed for processing MIMO RIRs with the aim of revealing valuable information about acoustic reflections paths are evaluated.

Far-field criterion for spherical microphone arrays and directional sources

A planar wavefront assumption facilitates significant simplifications in microphone array processing algorithms because information on the distance of the source is not required. This assumption was studied and formulated for spherical microphone arrays and point sources, but has not been studied yet for directional sources, which represent realistic sources such as musical instruments. A far-field criterion for directional sources is proposed in this paper, and the accuracy of a plane-wave approximation at a spherical microphone array is shown to depend on parameters of the acoustic configuration, such as the distance between the source and the microphone array and the source directivity.

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.

Spherical loudspeaker array beamforming in enclosed sound fields by MIMO optimization

Spherical loudspeaker arrays have been recently studied for a variety of applications such as spatial sound reproduction and room acoustics. Array directivity is typically designed for free field, although loudspeaker arrays often operate in enclosures. Therefore, current methods for directivity design may not be suitable. We present a new method for designing loudspeaker array directivity in enclosures, where the direct sound measured by a microphone array is emphasized compared to room reflections. The two spherical arrays form an acoustic multiple-input multiple-output (MIMO) system for which the loudspeaker array beamforming coefficients are designed based on the system transfer matrix. The proposed method uses the average output of the microphone array, over all look directions to avoid signal cancellation due to room reflections. The performance of the proposed method is studied through a simulation example.