This paper presents a gradient-based method for on-the-fly optimization for both per-frame and per-frequency window length of the short-time Fourier transform (STFT), related to previous work in which we developed a differentiable version of STFT by making the window length a continuous parameter. The resulting differentiable adaptive STFT possesses commendable properties, such as the ability to adapt in the same time-frequency representation to both transient and stationary components, while being easily optimized by gradient descent. We validate the performance of our method in vibration analysis.
INRIA（法国国家信息与自动化研究所）；PSL Research University（巴黎文理研究大学）；Safran Tech（赛峰科技）；Groupe Safran（赛峰集团）
In this paper, we revisit the use of spectrograms in neural networks, by making the window length a continuous parameter optimizable by gradient descent instead of an empirically tuned integer-valued hyperparameter. The contribution is mostly theoretical at this point, but plugging the modified STFT into any existing neural network is straightforward. We first define a differentiable version of the STFT in the case where local bins centers are fixed and independent of the window length parameter. We then discuss the more difficult case where the window length affects the position and number of…
In this paper, all-optical short-time Fourier transform (STFT) based on stimulated Brillouin scattering (SBS) is proposed and further used for real-time time-frequency analysis of different radio frequency (RF) signals. In the proposed all-optical STFT system, SBS not only provides a band-pass filter for implementing the window function in conjunction with a periodic frequency-sweep optical signal but also obtains the frequency domain information in different time windows through the generated waveform via frequency-to-time mapping (FTTM). A periodic frequency-sweep optical signal is generated…
The short-time Fourier transform (STFT), or the discrete Gabor transform (DGT), has been extensively used in signal analysis and processing. Their properties are characterized by a window function. For signal processing, designing a special window called tight window is important because it is known to make DGT-domain processing robust to error. In this paper, we propose a method of designing tight windows that minimize the sidelobe energy. It is formulated as a constrained spectral concentration problem, and a Newton's method on an oblique manifold is derived to efficiently obtain a solution.…
Modulated differentiable STFT and balanced spectrum metric for freight train wheelset bearing cross-machine transfer monitoring under speed fluctuations
State Key Laboratory of Advanced Rail Autonomous Operation（先进轨道交通自主运行状态重点实验室）；Beijing Jiaotong University（北京交通大学）；School of Mechanical, Electronic and Control Engineering（机械电子控制工程学院）
With the wide application of spectral and algebraic theory in discrete signal processing techniques in the field of graph signal processing, an increasing number of signal processing methods have been proposed, such as the graph Fourier transform, graph wavelet transform and windowed graph Fourier transform. In this paper, we propose and design the definition of the discrete linear canonical transform on graphs (GLCT), which is an extension of the discrete linear canonical transform (DLCT), just as the graph Fourier transform (GFT) is an extension of the discrete Fourier transform (DFT). First…
