  Many neural speech enhancement and source separation systems operate in the
time-frequency domain. Such models often benefit from making their Short-Time
Fourier Transform (STFT) front-ends trainable. In current literature, these are
implemented as large Discrete Fourier Transform matrices; which are
prohibitively inefficient for low-compute systems. We present an efficient,
trainable front-end based on the butterfly mechanism to compute the Fast
Fourier Transform, and show its accuracy and efficiency benefits for
low-compute neural speech enhancement models. We also explore the effects of
making the STFT window trainable.
