Learnable Wavelet Packet Transform for Data-Adapted Spectrograms

Capturing high-frequency data on the condition of complex systems, e.g. by acoustic monitoring, has increasingly become more prevalent. Such high-frequency signals contain typically time dependencies ranging over different time scales and different types of cyclic behaviors. Processing such signals requires careful feature engineering, in particular extracting meaningful time-frequency features. This can be time consuming and the performance is often dependend on the parameters choice. To address these limitations, we propose a deep learning framework for learnable wavelet packet transforms enabling to learn features automatically from data and optimize 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 the performance of the proposed approach by evaluating its improved spectral leakage and by applying it to an anomaly detection task for acoustic monitoring.