A spherical wave expansion for a steerable parametric array loudspeaker using Zernike polynomials

Author:

Zhong Jiaxin1ORCID,Kirby Ray1ORCID,Karimi Mahmoud1ORCID,Zou Haishan2ORCID

Affiliation:

1. Centre for Audio, Acoustics and Vibration, University of Technology Sydney, New South Wales 2007, Australia

2. Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing 210093, China

Abstract

A steerable parametric array loudspeaker (PAL) can electronically steer highly directional audio beams in the desired direction. The challenge of modelling a steerable PAL is to obtain the audio sound pressure in both near and far fields with a low computational load. To address this issue, an extension of the spherical wave expansion is proposed in this paper. The steerable velocity profile on the radiation surface is expanded as Zernike polynomials which are an orthogonal and form a complete set over a unit circle. An expression for the radiated audio sound is then obtained using a superposition of Zernike modes. Compared to the existing methods, the proposed expansion is computationally efficient and provides a rigorous transformation of the quasilinear solution of the Westervelt equation without paraxial approximations. The proposed expansion is further extended to accommodate local effects by using an algebraic correction to the Westervelt equation. Numerical results for steering single and dual beams are presented and discussed. It is shown that the single beam can be steered in the desired direction in both near and far fields. However, dual beams cannot be well separated in the near field, which cannot be predicted by the existing far field models.

Publisher

Acoustical Society of America (ASA)

Subject

Acoustics and Ultrasonics,Arts and Humanities (miscellaneous)

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