  In this paper, we propose a differentiable version of the short-time Fourier
transform (STFT) that allows for gradient-based optimization of the hop length
or the frame temporal position by making these parameters continuous. Our
approach provides improved control over the temporal positioning of frames, as
the continuous nature of the hop length allows for a more finely-tuned
optimization. Furthermore, our contribution enables the use of optimization
methods such as gradient descent, which are more computationally efficient than
conventional discrete optimization methods. Our differentiable STFT can also be
easily integrated into existing algorithms and neural networks. We present a
simulated illustration to demonstrate the efficacy of our approach and to
garner interest from the research community.
