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Acquired electrical waveforms can be affected by white noise. The 1-st part of the paper analysis deals with the denoising of multi-period steady signals by using 3 methods: mean signal method, an original method relying on wavelet packet trees and the method implemented by the wavelet-based Matlab function wden. The signal length influence over the mean signal method’s accuracy is studied. The results yielded by the other 2 methods are also analyzed considering signals with 7 periods. Afterward the wavelet-based methods are used to denoise segments of 7 periods with linearly variable magnitudes (ascending or descending) for 3 different slopes. Artificial test signals, with rich harmonic content, were used. They were polluted by sets of 10 white noises with different powers. Maximum absolute deviations and mean square root deviations were computed considering the original signals, before pollution, versus the corresponding denoised signal. The metrics were computed relative to the maximum absolute value of the noise and allowed to determine the most accurate method.

Wavelet packet trees represent a topic which grows in popularity when it comes to analysis of electrical waveforms. It allows for time-frequency analysis providing information on narrower ranges of frequency (as compared to the faster Discrete Wavelet Decomposition), but the computational resources are significantly greater than that involved in other types of wavelet-based analysis. In order to allow for this type of analysis to be usable in real-time applications, that is – to reduce the runtime, original algorithms were conceived and tested. In the first part of this work, previously implemented algorithms are briefly described, along with their pros and cons. Afterward, a new runtime optimization algorithm is proposed. Details on data structures, workflow, tests and study of errors are provided. This algorithm diminishes with up to 59% the runtime required by the application of the superposition theorem in order to evaluate the contribution of clustered harmonics using WPT.

Signals acquired from an industrial environment with many sources of electromagnetic interferences may be polluted by white noise. Polluted data segments with many steady consecutive periods can be used (sometimes unsuccessful) for the estimation of a denoised period from the steady acquired data by using the mean signal method. For data segments with at least 4 periods, when only certain segments (shorter than a period) can be considered steady, hybrid algorithms can be used to automatically evaluate the power of noise and afterward to perform the noise removal by using wavelet thrashing trees. This paper deals with 2 additional denoising techniques. The 1-st one is based on the Wavelet Package Transform and allows for the separation of the noise components which pollute a data segment of at least one period. The second approached denoising technique is also addressing one period data segments and estimates firstly the power of noise by using the energies of the vectors of details from the first 2 levels of a tree used by decompositions with the Stationary Wavelet Transform. The estimated power of noise is afterward used to establish the number of levels in the wavelet thrashing trees. In this last stage, two wavelet mothers were used. Simulated and real test signals were used and performance comparisons were performed.