Gabor Transform, Gabor-Wigner Transform and SPWVD as a time-frequency analysis of power quality

Abstract

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.