Time Domain Sampling of the Radial Functions in Spherical Harmonics Expansions

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