A Noniterative Method for Reconstruction of Phase From STFT Magnitude

A noniterative method for the reconstruction of the short-time fourier transform (STFT) phase from the magnitude is presented. The method is based on the direct relationship between the partial derivatives of the phase and the logarithm of the magnitude of the un-sampled STFT with respect to the Gau...

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Bibliographic Details
Published in:IEEE/ACM transactions on audio, speech, and language processing speech, and language processing, 2017-05, Vol.25 (5), p.1154-1164
Main Authors: Prusa, Zdenek, Balazs, Peter, Sondergaard, Peter Lempel
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Audio signals
Fourier transforms
Gabor transform
Gabor transformation
gradient theorem
numerical integration
phase reconstruction
Phase transitions
Reconstruction
Redundancy
Speech
Speech processing
STFT
Time-frequency analysis
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Summary:A noniterative method for the reconstruction of the short-time fourier transform (STFT) phase from the magnitude is presented. The method is based on the direct relationship between the partial derivatives of the phase and the logarithm of the magnitude of the un-sampled STFT with respect to the Gaussian window. Although the theory holds in the continuous setting only, the experiments show that the algorithm performs well even in the discretized setting (discrete Gabor transform) with low redundancy using the sampled Gaussian window, the truncated Gaussian window and even other compactly supported windows such as the Hann window. Due to the noniterative nature, the algorithm is very fast and it is suitable for long audio signals. Moreover, solutions of iterative phase reconstruction algorithms can be improved considerably by initializing them with the phase estimate provided by the present algorithm. We present an extensive comparison with the state-of-the-art algorithms in a reproducible manner.
ISSN:2329-9290
2329-9304
DOI:10.1109/TASLP.2017.2678166