Analyzing the Influence of Harmonic Parameters on Accuracy Indices When Applying Wavelet Transform

Abstract

The paper deals with the evaluation of root mean square deviations and maximum absolute relative errors associated to the decomposition followed by recomposition based on Wavelet Packet Transform (WPT) of signals pol-luted with harmonics. Subtrees associated to sets of harmonics presenting practical interest for industrial applications are addressed. The study uses artificial signals generated through the superposition of perfect sinusoids with pairs of harmonics which proved to be related in an almost exclusive manner to pairs of nodes from the bottom level of a WPT tree. 4 parameters had to be considered when determining the maximum and minimum values of errors for each set: the clustered harmonics’ magnitudes and their phase-shifts relative to the component of fundamental frequency. The decomposition/recomposition are time-efficient due to an original system of flags labeling each node from the WPT tree. For each analyzed set of harmonics, 3d graphical representation of minimum and maximum errors along with the associated 3d graphical representation of the phase-shifts are provided. At the same time, per set limits of errors ranges were established and discussed while specific patterns were deduced for the context in which extreme errors appear (phase-shifts and harmonic magnitudes). The results were commented, and conclusions were drawn.