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

arXiv: https://arxiv.org/abs/1609.00291 · HTML: https://mlsanity.com/paper/1609.00291/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2016.

## Built on by (most cited first, 7 of 7)

- [DiffPhase: Generative Diffusion-based STFT Phase Retrieval](https://mlsanity.com/paper/2211.04332/) (2022)
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- [Towards Controllable Audio Texture Morphing](https://mlsanity.com/paper/2304.11648/) (2023)
- [Example-Based Framework for Perceptually Guided Audio Texture Generation](https://mlsanity.com/paper/2308.11859/) (2023)
- [Unified Signal Compression Using a GAN with Iterative Latent Representation Optimization](https://mlsanity.com/paper/2109.11168/) (2021)
- [SpecSinGAN: Sound Effect Variation Synthesis Using Single-Image GANs](https://mlsanity.com/paper/2110.07311/) (2021)
- [Efficient Neural and Numerical Methods for High-Quality Online Speech Spectrogram Inversion via Gradient Theorem](https://mlsanity.com/paper/2505.24498/) (2025)

## Abstract (arXiv)

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.