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A spherical expansion for audio sounds generated by a circular parametric array loudspeaker.

Jiaxin Zhong1, Ray Kirby1, Xiaojun Qiu1

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

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|June 4, 2020
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Summary
This summary is machine-generated.

Calculating non-paraxial audio from parametric array loudspeakers (PALs) is simplified. A new spherical harmonics method offers a rigorous and efficient solution, achieving results 15x faster than previous methods.

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Area of Science:

  • Acoustics
  • Signal Processing
  • Computational Physics

Background:

  • Calculating non-paraxial sound from parametric array loudspeakers (PALs) is computationally intensive due to complex integrals.
  • Existing methods struggle with efficiency and accuracy for real-world applications.

Purpose of the Study:

  • To develop a rigorous and computationally efficient method for calculating non-paraxial sound fields from circular PALs.
  • To simplify the complex Westervelt equation solution for improved performance.

Main Methods:

  • Applied spherical harmonics expansion to the Westervelt equation under quasilinear approximation.
  • Decomposed the solution into uncoupled angular (Legendre polynomials) and radial (spherical Bessel functions) components.
  • Developed a series of threefold summations for efficient calculation.

Main Results:

  • The proposed method rigorously solves the Westervelt equation for circular PALs.
  • The solution simplifies to rapidly converging summations, significantly reducing computational load.
  • Simulations confirm accuracy comparable to direct integration but with over 15x speed improvement.

Conclusions:

  • The spherical harmonics expansion provides an exact and efficient solution for non-paraxial sound from PALs.
  • This method overcomes the computational limitations of existing approaches.
  • Enables faster and more accurate acoustic simulations for PAL systems.