This paper presents a discrete-time model of the spherical harmonics expansion describing a sound field. The so-called radial functions are realized as digital filters, which characterize the spatial
impulse responses of the individual harmonic orders. The filter
coefficients are derived from the analytical expressions of the timedomain radial functions, which have a finite extent in time. Due
to the varying degrees of discontinuities occurring at their edges, a
time-domain sampling of the radial functions gives rise to aliasing.
In order to reduce the aliasing distortion, the discontinuities are replaced with the higher-order anti-derivatives of a band-limited step
function. The improved spectral accuracy is demonstrated by numerical evaluation. The proposed discrete-time sound field model
is applicable in broadband applications such as spatial sound reproduction and active noise control.