Download Higher-Order Anti-Derivatives of Band Limited Step Functions for the Design of Radial Filters in Spherical Harmonics Expansions 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.
Download Band-Limited Impulse Invariance Method Using Lagrange Kernels The band-limited impulse invariance method is a recently proposed approach for the discrete-time modeling of an LTI continuoustime system. Both the magnitude and phase responses are accurately modeled by means of discrete-time filters. It is an extension of the conventional impulse invariance method, which is based on the time-domain sampling of the continuous-time response. The resulting IIR filter typically exhibits spectral aliasing artifacts. In the band-limited impulse invariance method, an FIR filter is combined in parallel with the IIR filter, in such a way that the frequency response of the FIR part reduces the aliasing contributions. This method was shown to improve the frequency-domain accuracy while maintaining the compact temporal structure of the discrete-time model. In this paper, a new version of the bandlimited impulse invariance method is introduced, where the FIR coefficients are derived in closed form by examining the discontinuities that occur in the continuous-time domain. An analytical anti-aliasing filtering is performed by replacing the discontinuities with band-limited transients. The band-limited discontinuities are designed by using the anti-derivatives of the Lagrange interpolation kernel. The proposed method is demonstrated by a wave scattering example, where the acoustical impulse responses on a rigid spherical scatter are simulated.