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Personal Sound Zones and Shielded Localized Communication through Active Acoustic Control

Neil Jerome A. Egarguin, Daniel Onofrei

TL;DR

The paper develops a time-domain extension of active Helmholtz-field control using an array of almost non-radiating sources to realize prescribed fields in interior control regions while suppressing exterior radiation. By formulating field synthesis as a boundary-input problem and employing a Fourier-synthesis framework with a fictitious null sphere, it enables two practical scenarios: personal sound zones in car cabins and shielded localized communications. The authors establish existence and stability for the control densities, implement a collocation-based numerical scheme with Tikhonov regularization, and demonstrate through multi-frequency and time-domain simulations that near-perfect field matching can be achieved in the control regions with rapid decay outside, avoiding complex boundary modeling. The approach offers a path toward stable, tunable, and decoupled acoustic control in enclosed environments and free space, with potential extensions to ocean acoustics and electromagnetic waves, and discussions on realizability using advanced transducers.

Abstract

In this paper, we present a time domain extension of our strategy on manipulating radiated scalar Helmholtz fields and discuss two important applied scenarios, namely (1) creating personal sound zones inside a bounded domain and (2) shielded localized communication. Our strategy is based on the authors' previous works establishing the possibility and stability of controlling acoustic fields using an array of almost non-radiating coupling sources and presents a detailed Fourier synthesis approach towards a time-domain effect. We require that the array of acoustic sources creates the desired fields on the control regions while maintaining a zero field beyond a larger circumscribed sphere. This paper recalls the main theoretical results then presents the underlying Fourier synthesis paradigm and show, through relevant simulations, the performance of our strategy.

Personal Sound Zones and Shielded Localized Communication through Active Acoustic Control

TL;DR

The paper develops a time-domain extension of active Helmholtz-field control using an array of almost non-radiating sources to realize prescribed fields in interior control regions while suppressing exterior radiation. By formulating field synthesis as a boundary-input problem and employing a Fourier-synthesis framework with a fictitious null sphere, it enables two practical scenarios: personal sound zones in car cabins and shielded localized communications. The authors establish existence and stability for the control densities, implement a collocation-based numerical scheme with Tikhonov regularization, and demonstrate through multi-frequency and time-domain simulations that near-perfect field matching can be achieved in the control regions with rapid decay outside, avoiding complex boundary modeling. The approach offers a path toward stable, tunable, and decoupled acoustic control in enclosed environments and free space, with potential extensions to ocean acoustics and electromagnetic waves, and discussions on realizability using advanced transducers.

Abstract

In this paper, we present a time domain extension of our strategy on manipulating radiated scalar Helmholtz fields and discuss two important applied scenarios, namely (1) creating personal sound zones inside a bounded domain and (2) shielded localized communication. Our strategy is based on the authors' previous works establishing the possibility and stability of controlling acoustic fields using an array of almost non-radiating coupling sources and presents a detailed Fourier synthesis approach towards a time-domain effect. We require that the array of acoustic sources creates the desired fields on the control regions while maintaining a zero field beyond a larger circumscribed sphere. This paper recalls the main theoretical results then presents the underlying Fourier synthesis paradigm and show, through relevant simulations, the performance of our strategy.

Paper Structure

This paper contains 12 sections, 2 theorems, 31 equations, 25 figures.

Table of Contents

  1. Introduction
  2. Statement of the Problem
  3. Mathematical Framework
  4. Numerical Framework
  5. Numerical Simulations
  6. Personal Sound Zones in Car Cabins
  7. Multi-frequency Simulation
  8. Time-domain Framework
  9. Time-domain Simulation
  10. Shielded Localized Communications
  11. Time-domain Simulations: Shielded Localized Communications
  12. Conclusion and future works

Key Result

Theorem 3.1

[EgarguinWM2020, Theorem 2.2] The compact operator ${\mathcal{D}}$ has a dense range.

Figures (25)

  • Figure 1: Personal Sound Zones in a Car Cabin: In this application, we create sound profiles in the control regions inside the blue spheres using the speakers drawn as red dots
  • Figure 2: Shielded Localized Communication: In this application, we create a desired sound profile in the near control using the sources while requiring the acoustic field to decay fast
  • Figure 3: An abstraction of the car cabin environment, the solid rectangle represents the enclosure of the cabin while the dots represent the control regions and the orange sphere represents the null sphere
  • Figure 4: A visual comparison of the real part of the prescribed and generated fields
  • Figure 5: Plot of the pointwise relative error
  • ...and 20 more figures

Theorems & Definitions (2)

  • Theorem 3.1
  • Theorem 3.2