A study on coherence between virtual signal and physical signals in remote acoustic sensing

Remote acoustic sensing can be used to estimate the error signals in human ears without placing any physical microphones there. In this paper, the coherence between the signals picked up by physical microphones over a sphere surface and the signal obtained at the sphere center is investigated. Based on the multiple channel coherence formulas in the time domain and frequency domain, the relationship between the coherence and the placement of physical microphones is analyzed by numerical simulations first, then the experimental results obtained in a reverberation chamber and a car cabin are presented to verify the simulation results. Finally, a placement of physical microphones for active control of road noise in car cabins is discussed. Both the numerical and experimental results show that an upper limit frequency exists for accurate sound pressure estimation at the center of a sphere with the sound pressure on the sphere surface. For a sufficiently complex sound field such as that in a reverberation room or in a car, half the wavelength of the upper limit frequency is about the average distance among the physical microphones.