High-frequency phase reconstruction is a challenging task in speech super-resolution. Recent studies suggest that the choice of window function is essential for phase estimation. Motivated by this, we investigate the effects of window functions on amplitude and phase reconstruction, and conclude that the optimized window functions should differ. So, we propose a dual-window diffusion method in which the amplitude and phase are estimated using their respective optimal window functions. However, direct signal reconstruction is challenging due to the window mismatch. To address this, we propose an alternating direction method of multipliers (ADMM)-based algorithm that recovers a signal by simultaneously satisfying the amplitude and phase constraints of the respective windows. Experimental results demonstrate that the proposed methods significantly improve perceptual quality compared to baseline methods.
Yan et al. (Thu,) studied this question.