Speaker
Description
Radial filters are required to transform the spherical harmonic coefficients of the pressure measured by a rigid-sphere microphone array into those of the plane-wave density representation of the measured sound field. Ideal radial filters exhibit poles at the origin, resulting in strong low-frequency amplification and numerical instability. To address this issue, regularization schemes are commonly applied, the most widely used being Tikhonov regularisation. It is shown that, at low frequencies, the Tikhonov regularisation filter for the n-th spherical harmonic order is equivalent to a zero-phase system obtained by applying an n-th order Butterworth high-pass filter in forward and reverse directions. Furthermore, explicit relationships are derived between the regularization parameter β, the corresponding Butterworth cut-off frequency, and the maximum magnitude of the resulting radial filter.