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

Area of Science:

• Acoustics
• Signal Processing
• Computational Physics

Background:

• Steerable parametric array loudspeakers (PALs) offer directional audio control.
• Accurate modeling of PALs in both near and far fields with low computational cost is challenging.
• Existing models often lack accuracy in near-field predictions or rely on paraxial approximations.

Purpose of the Study:

• To develop a computationally efficient and accurate model for steerable PALs.
• To extend spherical wave expansion for modeling audio sound pressure.
• To validate the model's performance for single and dual beam steering.

Main Methods:

• Proposed an extension of spherical wave expansion using Zernike polynomials to represent the velocity profile on the radiation surface.
• Derived an expression for radiated audio sound via superposition of Zernike modes.
• Incorporated algebraic correction to the Westervelt equation for local effects, avoiding paraxial approximations.

Main Results:

• The Zernike expansion model accurately predicts audio sound pressure in both near and far fields for single beams.
• Demonstrated computational efficiency compared to existing methods.
• Revealed limitations of far-field models by showing dual beams are not well-separated in the near field with the proposed method.

Conclusions:

• The proposed Zernike polynomial expansion provides a computationally efficient and rigorous method for modeling steerable PALs.
• The model accurately predicts single-beam steering in near and far fields.
• The study highlights the inability of existing far-field models to predict near-field dual-beam separation issues.