Sharp directivity function based on Fourier series expansion and its directional system realization with small number of microphones

In order that speech recognition system may. have a high recognition rate i n a noisy environment, a wide-band sharp directional microphone system is r equired at the input for securing a high S/N ratio. The authors have alread y reported the realization of a wide-band uni-directional microphone system by three-microphone integration method. In this paper, we intend to descri be the derivation of a sharp directivity function and the realization of it s microphone system. First, setting: the shape of the characteristic functi on to bring a sharp directional pattern and then expanding it into the Four ier series, we derive a new directivity function. Next, on the basis of thi s directivity function, we will present a sharp directional microphone syst em with only three non-directional microphones and the subsequent analog si gnal processing. And also, the directional pattern acquired by the proposed method and the effect of the dispersion in the sensitivity of the constitu ent microphones on the directivity are discussed in detail.