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


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 polluted 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  omponent 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 phaseshifts 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.