A Non-iterative Method for (Re)Construction of Phase from STFT Magnitude

TL;DR

This paper introduces a fast, non-iterative method for reconstructing phase from STFT magnitude, leveraging the relationship between phase derivatives and the magnitude's logarithm, effective even with discretized signals.

Contribution

It presents a novel direct approach for phase reconstruction from magnitude, improving speed and initialization for iterative algorithms, applicable to various window functions.

Findings

Performs well in discretized settings with low redundancy

Significantly speeds up phase reconstruction process

Enhances iterative algorithms with better initial phase estimates

Abstract

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.