Optimized use of Wavelet Packet Trees for the analysis of electrical waveforms

Abstract

Wavelet packet trees represent a topic which grows in popularity when it comes to analysis of electrical waveforms. It allows for time-frequency analysis providing information on narrower ranges of frequency (as compared to the faster Discrete Wavelet Decomposition), but the computational resources are significantly greater than that involved in other types of wavelet-based analysis. In order to allow for this type of analysis to be usable in real-time applications, that is – to reduce the runtime, original algorithms were conceived and tested. In the first part of this work, previously implemented algorithms are briefly described, along with their pros and cons. Afterward, a new runtime optimization algorithm is proposed. Details on data structures, workflow, tests and study of errors are provided. This algorithm diminishes with up to 59% the runtime required by the application of the superposition theorem in order to evaluate the contribution of clustered harmonics using WPT.