# Review of Advanced Implementation of Doppler Backscattering Method in Globus-M
## 2 Doppler Backscattering on Globus-M
### Data Analysis  
Table 2 provides the methods of analysis of DBS data that allowed one to investigate and determine the characteristics of plasma processes such as geodesic acoustic modes, limit cycle oscillations, quasi-coherent fluctuations, Alfven eigenmodes, turbulence, and filaments. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Notes** & **Field of Study** \\ \hline \multirow{3}{*}{Spectral analysis} & & geodesic acoustic modes, limit cycle \\  & connects the time domain and the frequency domain & oscillations, quasi-coherent \\  & & fluctuations, Alfven eigenmodes, \\  & & turbulences, filaments \\ \hline \multirow{3}{*}{Coherence analysis} & provides information on how & \\  & strongly two signals are & geodesic acoustic modes, \\  & correlated across a frequency & quasi-coherent fluctuations \\  & range & \\ \hline Correlation & information on radial correlation & geodesic acoustic modes, limit cycle \\  & properties of turbulence & oscillations, filaments \\ \hline \multirow{3}{*}{Bicoherent analysis} & frequencies at which nonlinear & geodesic acoustic modes, limit cycle \\  & interaction is most effective & oscillations, quasi-coherent \\ \cline{1-1}  & & fluctuations \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Methods applied to DBS signals to study various phenomena. Spectral analysis allows for the process of breaking down of any signal into its components at various frequencies, which is an important characteristic when it comes to turbulences and a large variety of instabilities. The Fourier transform (fast Fourier transform) provides this connection between the time domain and the frequency domain. There are various kinds of spectral analysis of the DBS signals available. They were applied to calculate the signal spectrum that describes the distribution of power into frequency components that the signal comprises. The fast Fourier transform is calculated in a window of a certain length that is chosen depending on the phenomenon being investigated. The window is then shifted by a time frame and the process continues. It was also possible to smooth these data so as to remove components of the background noise. Spectrograms were calculated as well in order to also have a visual representation of the spectrum as it changes in time. They are formed as the dependency of frequency on time while the power at each frequency at a given moment in time is represented by color. This is accomplished for the complex data of the DBS signals. The complex DBS signal spectrum is calculated so as to investigate the Doppler shift and consequently the rotation velocity. The velocity spectrum reveals some oscillatory phenomena. The modulus of the complex DBS signal showcases the behavior of the fluctuation amplitude. The calculation of the coherence spectrum leads to the examination of the relation between oscillations of various DBS signals. Correlation analysis of DBS signals can be used for obtaining information on radial correlation properties of turbulence and therefore on the turbulence spectrum with respect to radial wave numbers [34]. However for us the main goal was the detection of periodic components in the Doppler backscattering radiation, as well as the definition of the characteristics of such periodic processes. For this purpose, the calculation of cross-correlation functions (CCFs) between velocities measured at different radii or between amplitudes of DBS signals at different radii, and between the amplitude and velocity obtained at the same radius was performed. It was also possible to obtain correlation functions between the DBS signals and other diagnostic signals. The processes of coupling between spectral components of interacting waves could be revealed via bicoherence analysis.