Differentiable adaptive short-time Fourier transform with respect to the
  window length
Maxime Leiber Yosra Marnissi Axel Barrau Mohammed El Badaoui
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.