  Capturing high-frequency data concerning the condition of complex systems,
e.g. by acoustic monitoring, has become increasingly prevalent. Such
high-frequency signals typically contain time dependencies ranging over
different time scales and different types of cyclic behaviors. Processing such
signals requires careful feature engineering, particularly the extraction of
meaningful time-frequency features. This can be time-consuming and the
performance is often dependent on the choice of parameters. To address these
limitations, we propose a deep learning framework for learnable wavelet packet
transforms, enabling to learn features automatically from data and optimise
them with respect to the defined objective function. The learned features can
be represented as a spectrogram, containing the important time-frequency
information of the dataset. We evaluate the properties and performance of the
proposed approach by evaluating its improved spectral leakage and by applying
it to an anomaly detection task for acoustic monitoring.
