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Description
For a certain mode in spherical wave field expansions, a radial filter characterises the radially dependent diffraction phenomenon due to a spherical obstacle. Recently, a band-limited impulse invariance method (BLIIM) was proposed. It allows a more precise design of discrete-time filters for improved numerical simulations of such diffraction phenomena. However, for frequencies close to the Nyquist frequency and/or for high modal orders, BLIIM is numerically not straightforward or not feasible. Then, an optimisation-based infinite impulse response filter design with the continuous-time frequency response as target function, solving for the coefficients of the z-domain transfer function is one obvious workaround. An optimisation problem is exemplarily discussed for the radial filter occurring in the velocity-to-pressure spherical exterior expansion. This high-pass filter exhibits a steep slope and an extensively rippled pass band for a high modal order. The numerical experiments show that precise magnitude and phase responses of such radial filters can be achieved, requiring only some informed heuristics for the filter design parameters. The proposed approach outperforms IDFT-based frequency sampling, but not the BLIIM. The approach can be used where BLIIM is not feasible.