With the fast growing of deep neural network models, more and more tasks have been boosted when move on to deep models. Speech processing applications, e.g., speech enhancement, speech bandwidth expansion, dereverberataion, and etc., are also benefited. Most deep models focus more on improving the estimation of the spectral magnitude. However, there are evidences showing that the phase spectra are as well informative. Therefore, this dissertation investigates practical approaches to recover the spectral phase by resolving two inconsistency issues, i.e., frame-length inconsistency and frame-overlap inconsistency, leveraging the success of convex programming and alternating projection, respectively. Furthermore, frameworks to integrate both of the methods are explored. The proposed approaches and frameworks, taking advantage of some speech signal characteristics, have very limited number of assumptions, and therefore can be applied to various speech processing tasks.
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Some new applications of phase information to speech processing