Optimizing short-time Fourier transform parameters via gradient descent

The Short-Time Fourier Transform (STFT) has been a staple of signal processing, often being the first step for many audio tasks. A very familiar process when using the STFT is the search for the best STFT parameters, as they often have significant side effects if chosen poorly. These parameters are often defined in terms of an integer number of samples, which makes their optimization non-trivial. In this paper we show an approach that allows us to obtain a gradient for STFT parameters with respect to arbitrary cost functions, and thus enable the ability to employ gradient descent optimization of quantities like the STFT window length, or the STFT hop size. We do so for parameter values that stay constant throughout an input, but also for cases where these parameters have to dynamically change over time to accommodate varying signal characteristics.