Differentiable adaptive short-time Fourier transform with respect to the window length

This paper presents a method for on-the-fly gradient descent optimization for the 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 has commendable properties such as the ability to adapt in the same time-frequency representation to both transient and stationary components while being easily optmizable by gradient descent. We validate the performance of our method in vibration analysis.