PGHI: A Noniterative Method for Short-Time Fourier Transform Phase Reconstruction
What is PGHI?
PGHI is a noniterative method for the reconstruction of short-time Fourier transform (STFT) phase from its magnitude. By using the direct relationship between the partial derivatives of the phase and the logarithm of the magnitude of the STFT, this algorithm can produce a fast and efficient phase estimate. This approach is suitable for long audio signals and can even improve the solutions of iterative phase reconstruction algorithms by providing an accurate phase initialization.
How does PGHI work?
In the continuous setting, the 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 is used to derive the phase of the signal. In the discrete setting, where the discrete Gabor transform is used, this algorithm still performs well even with low redundancy using other windows, such as truncated Gaussian and Hann windows.
What are the benefits of PGHI?
One of the main benefits of PGHI is its noniterative nature, which makes it very fast and suitable for long audio signals. Additionally, solutions of iterative phase reconstruction algorithms can be improved considerably by initializing them with the phase estimate provided by the present algorithm.
An extensive comparison between PGHI and the state-of-the-art algorithms has been made in order to show that the proposed method performs very well, even in the discretized setting. Moreover, this algorithm is suitable for various types of audio signals, making it a versatile approach for phase reconstruction.
In this paper, we presented PGHI, a new noniterative method for the reconstruction of the STFT phase from its magnitude. The algorithm is based on the direct relationship between the partial derivatives of the phase and the logarithm of the un-sampled STFT with respect to the Gaussian window. Our experiments show that the algorithm performs very well, even in the discrete setting with different types of windows, such as truncated Gaussian and Hann window.
PGHI is a fast and efficient approach to estimating the phase of audio signals and can also provide an accurate initialization for iterative phase reconstruction algorithms. Therefore, it is a useful tool for audio signal processing and has many real-world applications.
