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Further Investigations on the Design of Radial Filters for the Driving Functions of Near-Field Compensated Higher-Order Ambisonics

Analytic driving functions for Near-field Compensated Higher-order Ambisonics (NFC-HOA) are derived based on the spherical harmonics expansions of the desired sound field and the Green’s function that models the secondary sources. In the frequency domain, the radial part of the driving function is given as spherical Hankel functions and compensates the near-field effects of the secondary sources. By exploiting the polynomial expansion of the spherical Hankel functions, the radial filters can be implemented as cascaded biquad filters in the time domain, thereby reducing the computational complexity significantly. In this paper three practical issues regarding the design of the radial filters are addressed: pole-zero computation, pole-zero mapping, and gain normalization. Useful suggestions are given for improvements in terms of stability and numerical stability, which are demonstrated by numerical simulations.

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