Spherical harmonics representations are widely adopted in applications such as analysis, manipulation, and synthesis of wave fields that are either captured or simulated. Recent studies have shown that, for broadband fields, a time domain representation of spherical harmonics expansions can benefit from computational efficiency and favorable transient properties. For practical usage, an accurate discrete-time modeling of spherical harmonics expansions is indispensable. The main challenge is to model the so called radial functions which describe the radial and frequency dependencies. In homogeneous cases, they are commonly realized as finite impulse response filters where the coefficients are obtained by sampling the continuous-time representations. This article investigates the temporal and spectral properties of the resulting discrete-time radial functions. The spectral distortions caused by aliasing are evaluated both analytically and numerically, revealing the influence of the distance from the expansion center, sampling frequency, and fractional sample delay. It is also demonstrated how the aliasing can be reduced by employing a recently introduced band limitation method.

中文翻译：

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球谐展开式中径向函数的时域采样


球谐函数表示广泛应用于捕获或模拟的波场的分析、操纵和合成等应用中。最近的研究表明，对于宽带场，球谐展开式的时域表示可以受益于计算效率和有利的瞬态特性。对于实际应用，球谐函数展开式的精确离散时间建模是必不可少的。主要挑战是对描述径向和频率依赖性的所谓径向函数进行建模。在同质情况下，它们通常被实现为有限脉冲响应滤波器，其中系数是通过对连续时间表示进行采样而获得的。本文研究了所得离散时间径向函数的时间和频谱特性。对混叠引起的频谱失真进行了分析和数值评估，揭示了距扩展中心的距离、采样频率和分数采样延迟的影响。还演示了如何通过采用最近引入的频带限制方法来减少混叠。