Sound field simulation for circular array based on spatial circular convolution

We propose a sound field simulation method for a circular array. In a linear array, when the distance between the loudspeaker units is equal to the interval between the observation points on the lines paralleled to the array, the sound pressures on the observation line can be calculated by the spatial convolution of the set of transfer functions and loudspeakers' driving signals. To apply this idea to a circular array, we developed a simulation method with equiangular observation points on the circle. The spatial circular convolution without zero padding, which is necessary in a linear array, can be used with this method. By conducting convolution based on the fast Fourier transform (FFT), the computational complexity is greatly reduced. Moreover, assuming that non-active loudspeakers are included in the loudspeaker array, the proposed method can be applied to an unequal interval array. For example, when the number of observation points is set to 128 and the number of loudspeakers is set to 32, circular convolution with FFT reduces the computational complexity to 75% compared to the conventional method. In addition, we argue that this method can be applied to a room in which the first reflected sounds are reflected from the floor. The proposed method is useful for simulating the sound field for a circular array when the suitable spatial samplings of the circumferential and radial directions are set.