Analyzing Electromagnetic Interferences in Power Applications by Using Time-Efficient Joint Analysis Based on DWT and WPT Trees

Decompositions relying on trees used to implement the Wavelet Package Transform (WPT) provide numerous advantages but require a significant runtime. When the parameters of relatively narrows ranges of harmonic orders change, only few vectors from the final nodes and the vectors hosted by the associated parent nodes" from upper levels are affected. The counterpart decomposition relying on a tree which implements the Discrete Wavelet Transform (DWT) with the same number of levels requires a 20 times smaller runtime. An estimation of the energetic sensitivity of all DWT details vectors to harmonic orders from the interval [2,256] was made. Both types of trees were connected by means of harmonic orders affecting the levels in the DWT tree and terminal nodes in the WPT tree. Through an original labeling of the WPT nodes, 18 topologies of WPT subtrees were deduced. These subtrees correspond to individual levels or to pairs/triplets of adjacent levels from the DWT tree. Tests on synthetic and real signals validated the DWT/WPT trees based algorithm used to perform faster identification of harmonic orders whose magnitudes change from one period to another. Runtime savings varying from 90% to 10% were obtained.