The Single-layer Potential Approach Applied to Sound Field Synthesis Including Cases of Non-enclosing Distributions of Secondary Sources


The present dissertation treats the topic of sound field synthesis. The focus lies thereby on serving human listeners although the results can be also exploited in other applications such as underwater acoustics or ultrasonics. A fundamental formulation of the problem is derived based on standard integral equations and the single-layer potential approach is identified as a useful tool in order to derive a general solution. An explicit solution is derived exemplarily for inward-radiating spherical distributions of secondary sources. The drawback of the single-layer potential approach is the fact that it requires secondary source distributions which enclose the receiver volume. Extensions to the single-layer potential approach are proposed which allow for a derivation of explicit solutions for circular, planar, and linear distributions of secondary sources. Based on above described formulation it is shown that the two established analytical approaches of Wave Field Synthesis and Near-field Compensated Higher Order Ambisonics constitute specific solutions to the general problem which are covered by the single-layer potential solution and its extensions. The physical theory of the single-layer potential approach requires that the employed distributions of secondary sources are continuous. Such continuous distributions can not be implemented in practice with today’s available loudspeaker technology but discrete distributions of loudspeakers have to be used. The consequences of this spatial discretization of the secondary source distribution are analyzed in detail for all above mentioned geometries in different spatial frequency domains, in temporal frequency domain, and in time domain. Two fundamental results are derived: Firstly, the discretization leads to repetitions of the secondary source driving function in a spatial frequency domain which is determined by the geometry of the secondary source distribution under consideration. And secondly, the bandwidth of the driving function with respect to the according spatial frequency domain has essential influence on the properties of the synthesized sound field. As a consequence, the concept of categorizing sound field synthesis approaches according to the bandwidth of the driving function into narrowband, wideband, and fullband approaches is proposed. It is finally shown how different types of spatial bandwidth limitation can be employed in order to locally increase the accuracy of the synthesized sound field. This concept is termed local sound field synthesis. This thesis presents an instrumentalized analysis of the fundamental physical properties of the problem. Although the presented work aims at audio presentation to human listeners, perception can only be marginally be considered. However, care was taken that the results are presented such that they can be directly used as a basis for experimental perceptual evaluation.

About The Author

Jens Ahrens

Jens Ahrens

Jens Ahrens is Associate Professor at the Division of Applied Acoustics at Chalmers University of Technology in Gothenburg, Sweden. He received a Diplom in Electrical Engineering/Sound Engineering (equivalent to an M.Sc.) from Graz University of Technology and University of Music and Dramatic Arts Graz, Austria, in 2005 and the Doctoral Degree (Dr.-Ing.) from University of Technology Berlin, Germany, in 2010. From 2006 to 2011, he was member of the Audio Technology Group at Deutsche Telekom Laboratories / TU Berlin where he worked on the topic of sound field synthesis. From 2011 to 2013 he was a Postdoctoral Researcher at Microsoft Research in Redmond, Washington, USA, after which he re-joined the Quality and Usability Lab at University of Technology Berlin. In the fall/winter terms 2015/16, he was Visiting Scholar at the Center for Computer Research in Music and Acoustics (CCRMA) at Stanford University.
Work Address

Jens Ahrens
Division of Applied Acoustics
Department of Civil and Environmental Engineering
SE-41296 Gothenburg