# Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review
## 3 Wavelet Transformation for Non-Stationary Time-Series: State-of-the-Art  
This section reviews the applications of WT in different fields. The wavelet applications are summarized in Table 1. The related studies are compared in terms of field, data, the mother wavelet used, the application of WT types and the performance. \begin{table}
\begin{tabular}{l l l l} \hline
**Representative** & **Data** & **Application of Wavelet** & **Wavelet** & **Performance** \\
**References** & **Data** & **Application of Wavelet** & **Transform** & **Performance** \\ \hline \multicolumn{4}{c}{_Geo-sciences and Geophysics_} \\ \hline \multirow{8}{*}{[23-30]} & Deep-sea sediment record TS & \multirow{8}{*}{trend analysis} & CWT, DWT, \\  & monthly NHST & & XWT, \\  & MJO and ENSO TS & & \\  & the standardized time series & correlation and coherency & MODWT, \\  & of winter & cross-spectral analysis & Foster’s \\  & The standardized BMI percentile & wavelet based spatial & wavelet, \\  & time series & verification & [PERSON], \\  & Atmospheric and Oceanic dataset & & [PERSON] \\  & SST and NAO TS & & \\ \hline \multicolumn{4}{c}{_Remote sensing:Vegetation_} \\ \hline \multirow{8}{*}{[7, 31-40]} & NDVI MODIS data & \multirow{8}{*}{Multi-scale analysis} & MODWT \\  & EVI MODIS TS & & DWT \\  & NDVI eight day, MODIS LAI & & CWT \\  & eight-day and MODIS Albedo & & MKA \\  & 16-day composite data & Wavelet-based denoising & Coiflets \\  & AVHR/NDVI data in Spain area & Wavelet-based feature & Daubechies \\  & 1 Km AGC spot vegetation data & Trend analysis & Symlet \\  & Landsat NDVI TS and LST MODIS & Haar & \\  & EVI data coupled with quality & & [PERSON] \\  & assessment science data & & [PERSON] \\  & Simulated NDVI TS & & \\ \hline \end{tabular}
\end{table} 
Table 1: Details of the surveyed papers, including year of publication, authors, the field, the data, the selected WT, the application of WT and the performance. MSE: Mean Squared Error, MRE: Mean Relative Error, RE: Relative Error, RMSE: Root Mean Square Error, MAPE: Mean Absolute Percentage Error, ACF: Autocorrelation Function, EVI: Enhanced Vegetation Index, MODIS: Moderate-Resolution Imaging Spectroradiometer, NDVI: Normalized Vegetation Index, AGC: Apparent Green Cover, LAI: Leaf Area Index, AVHRR: Advanced Very High-Resolution Radiometer, EEG: Electroencephalography, ECG: Electrocardiogram, LST: Land Surface Temperature, MCSA: Motor Current Signature Analysis, SNR: Signal-to-Noise-Ratio, CR: Compression Ratio, PRD: Percent Root Mean Square Difference, FBSE: Fourier Bessel Series Expansion and PV: Solar Photovoltaic, SD: Standard Deviation, DJIA:the Dow Jones Industrial Average, NHST: Northern Hemisphere Surface Temperature, MJO: Madden Julian Oscillation, ENSO: EL Nino Southern Oscillation, SST: Sea Surface Temperature, NAO: North Atlantic Oscillation, BMI: Maximum annual Ice extent in the Baltic Sea. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Representative** & **Data** & **Application of Wavelet** & \begin{tabular}{} \end{tabular}  & **Performance** \\ \hline \hline
**References** & \multicolumn{4}{c}{_Engineering_} \\ \hline
**Cutting strain in tool holder and motor current & & & CWT & \\
**Different simulated** & & Denoising & DWT & \\
**Single-degree-of-freedom systems** & & Feature extraction & MRA & \\
**and one experimental system.