The paper presents a general structural mathematical property of the wavelet packets, which can be used in various industrial applications, such as the identification of signals, fault detection, harmonic detection, denoising and more in general oscillation detection. In particular, possible algorithms based on this mathematical property can find application and be implemented in wavelets-based outlier packages. Some of these algorithms are currently being integrated into the Inferential Model Platform of the Advanced Control and Simulation Solution Responsible Unit within ABB's Industry division. AMS Subject Classification: 94A12, 65T60, 60G35