Wavelength proportional arrangement of virtual microphones based on interpolation/extrapolation for underdetermined speech enhancement

We previously proposed the virtual microphone technique to improve the speech enhancement performance in underdetermined situations, in which the number of channels is virtually increased by estimating extra observed signals at arbitrary positions along the straight line formed by real microphones. In our previous work, the effectiveness of the interpolation of virtual microphone signals for speech enhancement was experimentally confirmed. In this study, to examine the effectiveness of the extrapolation of a virtual microphone in improving the speech enhancement performance, we apply this technique to speech enhancement using a maximum signal-to-noise ratio (SNR) beamformer. Next, to improve the speech enhancement performance on the basis of the virtual microphone technique, we propose a new arrangement where a virtual microphone is placed in a position proportional to the wavelength. From the results of an experiment in an underdetermined situation, we confirmed that the proposed method markedly improves speech enhancement performance. Moreover, we present directivity patterns to confirm the behavior of each method of positioning the virtual microphone.