Bessel Nulls Recovery in Spherical Microphone Arrays for Time-Limited Signals

Spherical microphone arrays have recently been developed for a wide range of applications. In particular, scanning arrays in open-sphere configuration have been employed for room acoustics analysis, based on room impulse response measurements. However, it has been shown that the simple single-sphere configuration suffers from ill-conditioning around the zeros of the spherical Bessel function, and so alternative configurations, typically more complex, such as dual-sphere and single-sphere with cardioid microphones, have been proposed to overcome the effect of the Bessel nulls. This paper shows that in the particular case of time-limited signals, for example in room impulse response measurements, the ill-conditioning due to the spherical Bessel functions can be reduced using nonuniform sampling in the frequency domain. Following a presentation of the theory and a simulation study, an experimental example is presented for use of the method in a single-sphere measurement in an auditorium.