A Non-iterative Method for (Re)Construction of Phase from STFT Magnitude
This addresses the phase reconstruction problem in audio signal processing, offering a faster alternative to iterative methods, though it is incremental as it builds on existing theory.
The paper tackles the problem of reconstructing the Short-Time Fourier Transform (STFT) phase from its magnitude by introducing a non-iterative method based on partial derivatives, which is shown to be fast and effective even with discretized settings and low redundancy. The method improves iterative algorithms when used for initialization and performs competitively in comparisons with state-of-the-art approaches.
A non-iterative method for the construction 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 like the Hann window. Due to the non-iterative 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.