Computational Aspects Concerned with the Optimized Use of Wavelet Package Trees

Abstract

Decompositions of electric waveforms relying on the Wavelet Package Transform (WPT) provide numerous advantages but requires a significant amount of computational resources (runtime and memory). Previous study of some of the authors were concerned with special properties provided by the weights of energies supplied by odd harmonics in the final nodes of a WPT trees with 5 levels. New researches were made now considering the better sampling rate of modern data acquisition systems. Another topology, with 7 levels, was studied, and interesting results relative to much higher harmonic orders (up to the rank of 256) were obtained with respect to both even and odd harmonic orders. Studies on artificial waveforms polluted with a single harmonic were made firstly, revealing interesting aspects relative to clusters of nodes affected by the same group of harmonic orders. Different pairing patterns of odd and even harmonics were revealed, along with decisions on nodes being more relevant for certain harmonics. Afterward, studies on possible practical application of final nodes sensitivity to limited ranges of harmonic orders were made. The obtained results provide the support for simple computational techniques meant to reduce as much as possible the computational resources required by the WPT analysis.