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In this paper, we present a sound field interpolation for array signal processing (ASP) that is robust to rotation of a circular microphone array (CMA), and we evaluate beamforming as one of its applications. Most ASP methods assume a time-invariant acoustic transfer system (ATS) from sources to the microphone array. This assumption makes it challenging to perform ASP in real situations where sources and the microphone array can move. Therefore, considering a time-variant ATS is an essential task for the use of ASP. In this study, we focus on one such movement, the rotation of the CMA. Our method interpolates the sound field on the circumference of a circle, where microphones are equally spaced, based on the sampling theorem on the circle. The interpolation enables us to estimate the signals at the microphone positions before the rotation. Hence, conventional ASP, which assumes a time-invariant ATS, is applicable after interpolation without modification. We developed two beamforming schemes, one for batch and one for online processing, that combine the minimum power distortionless response beamformer and sound field interpolation. We evaluated the dependences of the interpolation on frequency and rotation angle using the signal-to-error ratio. Additionally, simulation results demonstrated that the two proposed schemes improve the beamformer's performance when the CMA rotates.

This paper presents improvements to two-stage algorithms for estimating the short-time Fourier transform (STFT) phase from only the amplitude by using deep neural networks (DNNs). The phase is difficult to reconstruct due to its sensitivity to the waveform shift and wrapping issue. To mitigate these problems, two-stage approaches indirectly estimate the phase through phase derivatives, i.e., instantaneous frequency (IF) and group delay (GD). In the first stage, the IF and GD are estimated from the amplitude using DNNs, and then in the second stage, the phase is reconstructed by maintaining the IF/GD information. Conventional methods for the second stage do not consider the importance of high-amplitude time-frequency bins, e.g., the least squares-based method, or lack a solid model, e.g., the average-based method. To address these problems, we propose improvements to the second stage of two-stage algorithms by using von Mises distribution-based maximum likelihood and weighted least squares. We also provide theoretical discussions for the phase reconstruction, including the investigations of the properties of the GD and roles of the IF/GD information in the inverse STFT. On the basis of the analysis, we propose a new phase-based feature, i.e., inter-frequency phase difference (IFPD), and demonstrate its application in two-stage phase reconstruction algorithms. We conducted subjective and objective experiments to compare the performances of our proposed and conventional methods. The results confirm that the proposed method using the IFPD performs better than other methods for all metrics.

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