# Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review
## 3 Wavelet Transformation for Non-Stationary Time-Series: State-of-the-Art
### Application of WT in Medicine  
In this subsection, the WT is presented in the analysis of bio-signals. In fact, two types of data, namely ECG and EEG signals, were basically studied. While EEG is a measure of the electrical activity associated with the heart, ECG is a graphical measure of the electrical activities in the human heart muscles. Both signals are non-stationary [80].  
[PERSON] [62] presented a review of the WT of the ECG signal. Several applications based on DWT and CWT, such as the detection of localized abnormality, ECG morphology, distortion and noise, were discussed. In addition, the authors concentrated on the heart rate variability and the cardiac arrhythmias. After 2005, there were a few works--for example, [PERSON] et al. [66] have applied the WT for denoising the EEG signal. Then, the CWT has been coupled with \(\beta\)-Hill climbing in order to find the optimal wavelet parameters when calculating the minimum MSE between the original and denoised ECG signals. To evaluate the performance of the proposed approach, the PRD and SNR have been calculated.  
In addition, the WT was investigated in several works to analyze the electroencephalography signals. For example, [PERSON] et al. [63] analyzed the EEG signal of the focal and non-focal groups to detect the epileptogenic area. The proposed approach was based on the empirical wavelet technique to decompose the original signal and to detect different rhythms. The Central Tendency Measure (CTM) parameter was used to estimate the area measured for various reconstructed phase spaces obtained from the rhythms. Finally, the least square support vector machine (LS-SVM) was used to classify the focal and non-focal groups of the EEG signal. Moreover, [PERSON] et al. [65] have used the wavelet-based filter bank in order to represent the multi-component synthetic signals and real EEG signals in the time-frequency domain. The method has been divided into four steps. First, the FBSE has been employed to represent the multi-component signal in the spectral domain. Then, to estimate the accuracy of the boundary frequency, the scale-based boundary detection method has been used. In addition, the WT has been applied to decompose the signal into narrow-band components. Finally, the MSE has been used to compare the proposed approach to the EWT and Hilbert-Huang Transform (HHT). Recently, [PERSON] et al. [64] have used different WT types in order to automatically detect and predict the seizure onset. The EEG data has been used with two datasets: Freiburg (intracranial EEG) and CHB-MIT (scalp EEG). The first step consists of denoising the EEG signal using the multiscale principal component analysis. Then, the EMD, DWT and WPD have been used to extract features from the denoised signal. After that, several classifiers, such as Random Forest (RF), Support Vector Machine (SVM), Multi-Layer Perceptron (MLP) and k-Nearest Neighbour (K-NN), have been tested for prediction purposes. Finally, several performance criteria, such as sensitivity, specificity and accuracy, have been used to calculate the performance of the different cases.