Diminishing the Computational Burden when Analyzing Electrical Signals with Long Wavelet Filters


Wavelet analysis is characterized by filters with irrational coefficients and runtimes increasing with filters order. The terminal nodes of Wavelet Packet decomposition trees exhibit good harmonics’ selectivity when implemented with Daubechies wavelet mothers with filters of length 28 and respectively of length 40 (denoted in MATLAB by ‘db14’ and ‘db20’). Therefore they can be used for power quality (PQ) analysis of electric signals. When rounded to 4 decimal places, certain coefficients from these filters become 0. In the “rounded” context, the number of iterations sup-porting the convolution products involved by the Wavelet analysis is restricted. Based on the number of neglected co-efficients and length of wavelet filter, a formula is deduced for the percent runtime savings strictly associated to the wavelet decompositions. Statistical evaluations (considering sets of 20 consecutive programs executions) were performed considering full operational contexts, where all types of studied wavelets were involved in complex operations like evaluating PQ indices and harmonic spectra. The mean runtime savings proved to be 20.4% for ‘db14’ and respec-tively 23.2% for ‘db20’. The impact of rounding over the PQ analysis’s accuracy was evaluated considering three-phase waveforms acquired from a power group. The follow-ing quantities were considered: harmonic spectra and ener-gies of the Wavelet Packet tree’s terminal nodes, instanta-neous values corresponding to the fundamental frequency, vectors of details and approximations yielded by the Dis-crete Wavelet Transform and signals reconstructed from the vectors of details and approximations. Highly acceptable small errors were obtained, recommending the rounding to 4 decimal places of the analyzed wavelet filters as a faster reliable wavelet based analysis method. images