Learnable Wavelet Packet Transform for Data-Adapted Spectrograms

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.