  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.
