Incorporating Source Directivity in Wave-based Virtual Acoustics: Time-domain Models and Fitting to Measured Data
Journal article, 2019

The modeling of source directivity is a problem of longstanding interest in virtual acoustics and auralisation. This remains the case for newer time domain volumetric wave-based approaches to simulation such as the finite difference time domain method. In this article, a spatio-temporal model of acoustic wave propagation, including a source term is presented. The source is modeled as a spatial Dirac delta function under the action of a series of differential operators associated with the spherical harmonic functions. Each term in the series gives rise to the directivity pattern of a given spherical harmonic, and is separately driven through a time domain filtering operation of an underlying source signal. Such a model is suitable for calibration against measured frequency-dependent directivity patterns and a procedure for arriving at time domain filters for each spherical harmonic channel is illustrated. It also yields a convenient framework for discretisation, and a simple strategy is presented, yielding a locally-defined operation over the spatial grid. Numerical results, illustrating various features of source directivity, including the comparison of measured and synthetic directivity patterns, are presented.

room acoustics

sound source directivity

spherical harmonics

Finite difference time domain


Stefan Bilbao

University of Edinburgh

Jens Ahrens

Chalmers, Architecture and Civil Engineering, Applied Acoustics

Brian Hamilton

University of Edinburgh

Journal of the Acoustical Society of America

0001-4966 (ISSN) 1520-8524 (eISSN)

Vol. 146 4 2692-2703

Areas of Advance

Information and Communication Technology

Subject Categories


Signal Processing





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