Wavelength-Proportional Interpolation and Extrapolation of Virtual Microphone for Underdetermined Speech Enhancement

We previously proposed the virtual microphone technique to improve speech enhancement performance in underdetermined situations, in which the number of channels is virtually increased by estimating extra microphone signals at arbitrary positions along the straight line formed by real microphones. The effectiveness of the interpolation of virtual microphone signals for speech enhancement was experimentally confirmed. In this work, we apply the extrapolation of a virtual microphone as preprocessing of the maximum signal-to-noise ratio (SNR) beamformer and compare its speech enhancement performance (the signal-to-distortion ratio (SDR) and signal-to-interference ratio (SIR)) with that of using the interpolation of a virtual microphone. Furthermore, we aim to improve speech enhancement performance by solving a trade-off relationship between performance at low and high frequencies, which can be controlled by adjusting the virtual microphone interval. We propose a new arrangement where a virtual microphone is placed at a distance from the reference real microphone proportional to the wavelength at each frequency. From the results of our experiment in an underdetermined situation, we confirmed speech enhancement performance using the extrapolation of a virtual microphone is higher than that of using the interpolation of a virtual microphone. Moreover, the proposed wavelength-proportional interpolation and extrapolation method improves speech enhancement performance compared with the interpolation and extrapolation. Furthermore, we present the directivity patterns of a spatial filter and confirmed the behavior that improves speech enhancement performance.