Online Phase Reconstruction via DNN-Based Phase Differences Estimation

Yoshiki Masuyama*, Kohei Yatabe, Kento Nagatomo, Yasuhiro Oikawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper presents a two-stage online phase reconstruction framework using causal deep neural networks (DNNs). Phase reconstruction is a task of recovering phase of the short-time Fourier transform (STFT) coefficients only from the corresponding magnitude. However, phase is sensitive to waveform shifts and not easy to estimate from the magnitude even with a DNN. To overcome this problem, we propose to use DNNs for estimating differences of phase between adjacent time-frequency bins. We show that convolutional neural networks are suitable for phase difference estimation, according to the theoretical relation between partial derivatives of STFT phase and magnitude. The estimated phase differences are used for reconstructing phase by solving a weighted least squares problem in a frame-by-frame manner. In contrast to existing DNN-based phase reconstruction methods, the proposed framework is causal and does not require any iterative procedure. The experiments showed that the proposed method outperforms existing online methods and a DNN-based method for phase reconstruction.

Original languageEnglish
Pages (from-to)163-176
Number of pages14
JournalIEEE/ACM Transactions on Audio Speech and Language Processing
Publication statusPublished - 2023
Externally publishedYes


  • Real-time spectrogram inversion
  • group delay
  • instantaneous frequency
  • low-latency
  • time-frequency analysis

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Acoustics and Ultrasonics
  • Computational Mathematics
  • Electrical and Electronic Engineering


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