# Application of Wavelet Transform and Fractal Analysis for
## 3 Results
#### Fractal Dimension  
In the second stage of the study, the self-similarity of the pH signals was investigated to confirm that it is possible to automatically classify patients into a specific group.  
It was assumed that the fractal properties of the pH time series obtained in the healthy persons are changed in the measurement data recorded in the subjects with the disorders resulting from diagnosed GERD. The methods of fractal statistics make it possible to study the correlations between the measured values at different levels of detail over the entire available time range of the signal under study.  
This study used the calculations of the gamma spectral exponent of the 1/f processes. This factor is characterised by a high sensitivity to subtle changes in the features of the 1/f process signal under study. The main assumption made by the authors was that the gamma spectral exponents determined for the pH signals with different total DeMeester scores should also be different.  
The values of the gamma exponents, for 24-h measurements of acid exposure, were determined according to Equation (1) using the DWT method. The gamma exponent can be graphically interpreted as the slope angle of the trend line for the points obtained from the discrete wavelet transform of the signal under study (Figure 11a). Figure 11b additionally shows box plots based on the fractal dimension analysis, illustrating the similarities and differences between the healthy and sick patients.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Successes/Attempts** \\ \hline Total success rate & 89.5\% & 17/19 \\ \hline Sensitivity & 93.33\% & 14/15 \\ \hline Specificity & 75\% & 3/4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters used to calculate the total DeMeester parameter.  
Figure 11: The calculation results of the spectral exponent \(\gamma\) and its statistical representation. (**a**) Distribution of the spectral exponent \(\gamma\) illustrated as a function of the decomposition level (the dashed line represents a trend line calculated by the method of least squares). (**b**) The minimum and maximum values of the spectral exponent gamma together with the first, second, and third quartiles associated with the two groups of patients.  
The analysis of the fractal calculation results, which are presented in Figure 11b, clearly shows that the healthy subjects (total DeMeester \(<15.9\)) have common features that differentiate them from the measurement data collected for the subjects diagnosed with GERD (total DeMeester \(>15.9\)). These results both confirm the validity of the assumptions made by the authors and indicate the superiority of the method presented earlier in this chapter, which was based on the use of CWT. This method allows not only a simple classification of the patients into sick or healthy groups but also an indication of the stage of the pathology. In addition, the results of the applied method do not require interpretation by a specialist, which significantly accelerates and simplifies the procedure of the preliminary diagnosis of the examined patient. The method also does not require sophisticated and high-performance computing equipment, which allows its potential implementation and application as early as the stage of real-time measurement data recording.