  For many machine learning applications, a common input representation is a
spectrogram. The underlying representation for a spectrogram is a short time
Fourier transform (STFT) which gives complex values. The spectrogram uses the
magnitude of these complex values, a commonly used detector. Modern machine
learning systems are commonly overparameterized, where possible
ill-conditioning problems are ameliorated by regularization. The common use of
rectified linear unit (ReLU) activation functions between layers of a deep net
has been shown to help this regularization, improving system performance. We
extend this idea of ReLU activation to detection for the complex STFT,
providing a simple-to-compute modified and regularized spectrogram, which
potentially results in better behaved training. We then confirmed the benefit
of this approach on a noisy acoustic data set used for a real-world
application. Generalization performance improved substantially. This approach
might benefit other applications which use time-frequency mappings, for
acoustic, audio, and other applications.
