Using the Wavelet Packet Transform to Evaluate Weights of Clustered Harmonics Using Lookup Tables

The paper deals with an original technique used to evaluate the weights of sets of harmonic orders (H1 and H2) clustered in an almost exclusive manner to pairs of terminal nodes from a Wavelet Packet Tree (WPT). The total harmonic contribution (SHIH2) of such harmonics can be retrieved from the analyzed signal by using original computational techniques. The total root mean square of SHIH2 can be used to deduce, by using a lookup table, a larger set of possible solutions in terms of harmonic weights for H1 and H2. This set can be afterward reduced by imposing conditions related to the energies of the associated terminal nodes, making use of another table. The final selection of the approximated solution relies on harmonic phase-shifts estimations provided by solutions of linear systems. The technique requires a highly acceptable small runtime while considering less complicated operations and is a good alternative for analysis of periods with non-symmetric half-periods.