The one-dimension frequency analysis based on DFT (Discrete FT) is sufficient in many cases in detecting power disturbances and evaluating power quality (PQ). To illustrate in a more comprehensive manner the character of the signal, time-frequency analyses are performed. The most common known time-frequency representations (TFR) are spectrogram (SPEC) and Gabor Transform (GT). However, the method has a relatively low time-frequency resolution. The other TFR: Discreet Dyadic Wavelet Transform (DDWT), Smoothed Pseudo Wigner-Ville Distribution (SPWVD) and new Gabor-Wigner Transform (GWT) are described in the paper. The main features of the transforms, on the basis of testing signals, are presented.

The application of power quality parameters measurement algorithms requires utilization of computational methods which transform the signal from the time- to the frequency-domain. Currently, the most frequently applied method is the fast Fourier transformation (FFT). Because of the amendment of the proper power quality standards, it is also necessary to consider of implementation discrete Fourier transformation (DFT) algorithms. Considering the number of computations, DFT is more complicated than FFT. This paper presents basic analog-to-digital conversion parameters, which are defined in the norms, the time duration analysis of DFT algorithms, considering described assumptions and comparing them to FFT. Codes created in C and assembler languages, as well as the Matlab/Simulink environment, were taken into account. The software including the aforementioned codes was implemented in a low-cost power quality measurement system based on the TMS320c6713 floating point DSP processor from Texas Instruments. In the software, a real time DSP/BIOS operation system was used. Multi thread programming in power quality measurement systems was presented, and an analysis of computational efficiencies of the systems based on the TMS320c6 713 DSP processors was performed.

Vibroarthrography (VAG) is a non-invasive and potentially widely available method supporting the joint diagnosis process. This research was conducted using VAG signals classified to five different condition classes: three stages of chondromalacia patellae, osteoarthritis, and control group (healthy knee joint). Ten new spectral features were proposed, distinguishing not only neighboring classes, but every class combination. Additionally, Frequency Range Maps were proposed as the frequency feature extraction visualization method. The results were compared to state-of-the-art frequency features using the Bhattacharyya coefficient and the set of ten different classification algorithms. All methods evaluating proposed features indicated the superiority of the new features compared to the state-of-the-art. In terms of Bhattacharyya coefficient, newly proposed features proved to be over 25% better, and the classification accuracy was on average 9% better.

The measurement algorithms applied in power quality measurement systems are based on Fourier Transformation (FT). The discrete versions of Fourier transformation - DFT (Discrete FT) and FFT (Fast Fourier Transformation) are most commonly used. That one-dimension frequency analysis is sufficient in many cases. However, to illustrate the character of the signal in a more comprehensive manner, it is crucial to represent the investigated signal on time-frequency plane. There are a lot of time-frequency representations (TFR) for presenting measured signal. The most common known are spectrogram (SPEC) and Gabor Transform (GT), which are based on direct DFT results. However, the method has relatively low time-frequency resolution. The other TFR representing Cohen class: Wigner-Ville Distribution (WVD) and its variants: Pseudo Wigner-Ville Distribution (PWVD), Smoothed Pseudo Wigner-Ville Distribution (SPWVD) and Gabor-Wigner Transform (GWT) are described in the paper. The main features of the transforms, on the basis of testing signals, were presented.

Electric arcing is a common problem in DC power systems. To overcome this problem, the electric arc detection algorithm has been developed as a faster alternative to existing algorithms. The following issues are addressed in this paper: The calculation of the proposed algorithm of incremental decomposition of the signal over time; the computational complexity of Fast Fourier Transform (FFT) and the incremental decomposition; the test bench used to measure electric arcs at given parameters; the analysis of measurements using FFT; and the analysis of measurements using incremental decomposition. The parameters are the DC voltage, electric load, and width of the gap between electrodes. The results showed that the proposed algorithm allows for a faster calculation—about seven times faster than FFT—and cheaper implementation in electric arc detection devices than FFT.

One of the most important classification problems is selecting proper features, i.e. features that describe the classified object in the most straightforward way possible. Then, one of the biggest challenges of the feature selection is the evaluation of the feature’s quality. There is a plethora of feature evaluation methods in the literature. This paper presents the results of a comparison between nine selected feature evaluation methods, both existing in literature and newly defined. To make a comparison, features from ten various sets were evaluated by every method. Then, from every feature set, best subset (according to each method) was chosen. Those subsets then were used to train a set of classifiers (including decision trees and forests, linear discriminant analysis, naive Bayes, support vector machines, k nearest neighbors and an artificial neural network). The maximum accuracy of those classifiers, as well as the standard deviation between their accuracies, were used as a quality measures of each particular method. Furthermore, it was determined, which method is the most universal in terms of the data set, i.e. for which method, obtained accuracies were dependent on the feature set the least. Finally, computation time of each method was compared. Results indicated that for applications with limited computational power, method based on the average overlap between feature’s values seem best suited. It led to high accuracies and proved to be fast to compute. However, if the data set is known to be normally distributed, method based on two-sample ${t}$ -test may be preferable.