  Phase reconstruction, which estimates phase from a given amplitude
spectrogram, is an active research field in acoustical signal processing with
many applications including audio synthesis. To take advantage of rich
knowledge from data, several studies presented deep neural network (DNN)--based
phase reconstruction methods. However, the training of a DNN for phase
reconstruction is not an easy task because phase is sensitive to the shift of a
waveform. To overcome this problem, we propose a DNN-based two-stage phase
reconstruction method. In the proposed method, DNNs estimate phase derivatives
instead of phase itself, which allows us to avoid the sensitivity problem.
Then, phase is recursively estimated based on the estimated derivatives, which
is named recurrent phase unwrapping (RPU). The experimental results confirm
that the proposed method outperformed the direct phase estimation by a DNN.
