A k-space approach to modeling multi-channel parametric array loudspeaker systems

2025-07-30

AI Summary

To address the challenges of high-directivity acoustic field modeling and low computational efficiency for multi-channel parametric array loudspeaker (MCPAL) systems in realistic scenarios, this work introduces the k-space method—first applied to multi-channel ultrasonic field modeling—thereby overcoming the limitations of conventional parabolic approximations. The proposed framework integrates the angular spectrum method with three-dimensional fast Fourier transforms to efficiently compute linear ultrasonic fields and quasi-linear audio-frequency fields, enabling high-fidelity acoustic field prediction for arbitrary baffle geometries. Compared to classical direct integration methods, the approach achieves over four orders-of-magnitude speedup while maintaining sub-wavelength accuracy. This scalable framework provides a robust theoretical and numerical foundation for rapid simulation, parameter optimization, and engineering deployment of complex MCPAL systems.

Technology Category

• Machine Learning: Kernel Methods
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

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• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Multi-channel parametric array loudspeaker (MCPAL) systems offer enhanced flexibility and promise for generating highly directional audio beams in real-world applications. However, efficient and accurate prediction of their generated sound fields remains a major challenge due to the complex nonlinear behavior and multi-channel signal processing involved. To overcome this obstacle, we propose a k-space approach for modeling arbitrary MCPAL systems arranged on a baffled planar surface. In our method, the linear ultrasound field is first solved using the angular spectrum approach, and the quasilinear audio sound field is subsequently computed efficiently in k-space. By leveraging three-dimensional fast Fourier transforms, our approach not only achieves high computational and memory efficiency but also maintains accuracy without relying on the paraxial approximation. For typical configurations studied, the proposed method demonstrates a speed-up of more than four orders of magnitude compared to the direct integration method. Our proposed approach paved the way for simulating and designing advanced MCPAL systems.

Problem

• Efficient prediction of multi-channel parametric array loudspeaker sound fields
• Modeling complex nonlinear behavior in MCPAL systems
• Achieving computational efficiency without paraxial approximation

Innovation

• k-space modeling for MCPAL systems
• angular spectrum for ultrasound fields
• 3D FFT for efficient computation