Notes

To analyze these disturbances, data are often available as a form of sampled time function that is represented by a time series of amplitudes. When dealing with such data, the Fourier transform (FT)-based approach is most often used. FT provides the frequency information; however, it is not capable of providing time information about signal disturbances. For instance, time-frequency information related to disturbance waveforms can be obtained by using the STFT [3], but transient signals cannot be adequately described with this transform due to a fixed window size and it suffers severely from the Heisenberg uncertainty principle [4], causing it to undergo a “trade-off” between time resolution and frequency resolution. To overcome the drawback of STFT, the WT provides the time-scale analysis of the non-stationary signal since it decomposes the signal into time-scale representation rather than time-frequency representation. This is one of the reasons for the creation of the wavelet transform (or multiresolution analysis in general), which can give good time resolution for high-frequency events, and good frequency resolution for low frequency events, which is the type of analysis best suited for many real signals. Wavelet transform [5], which is a popular signal analysis method, offers continuous and discrete wavelet transforms (CWT and DWT) [6] and wavelet packet transform (WPT) [7,8] for the feature extraction of signals. The analysis of a signal with the discrete wavelet transform (DWT) or the wavelet packet transform (WPT) requires a proper selection of mother wavelet, decomposition levels, and sampling frequency. The selection of these parameters, along with a suitable choice of a mother wavelet, differs for the signals containing different frequency components and this limits the application of WT and WPT to analyze real-time non-stationary signals. To overcome these drawbacks, various adaptive techniques have been proposed, such as the S-transform and recursive Newton-type algorithm [15]–[18], to assess the PQ indices for stationary and nonstationary signals. In the literature, parametric high-resolution