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.