In this chapter presents a methodology for assessment the power quality characteristics based on the concerted use of discrete Hilbert and Fourier transforms (DHT and DFT). A methodology feature is to reduce the effect of DFT leakage when processing DFT, for which an iterative method of refining the fundamental voltage frequency of the power grid is proposed. The method is implemented by resampling the sample in order to match the sampling time and sampling rate with the frequency of the fundamental harmonic of the supply voltage. This frequency is estimated by analyzing the voltage phase determined by DHT. The method makes it possible to determine the frequency of the fundamental harmonic with an error not exceeding 50 µHz. The considered methodology makes it possible to determine such power quality characteristics as the frequency of the fundamental harmonic and higher harmonics, the total harmonic distortion, the levels of individual higher harmonics, voltage dips, voltage swell, supply interruption, and voltage phase jumps during voltage dips. Power quality characteristics in the frequency domain are calculated on the basis of DFT, and in the time domain—on the basis of DHT.