# A Comparative Study of Signal Processing Methods for Contactless Geodetic Monitoring
## 3 Results  
The analysis of the measured signals was performed using the Fast Fourier Transformation (FFT) and the Lomb-Scargle periodogram (LS). The Blastware Advanced Module hardware was used to analyze the signals measured with the seismograph, and the GeoCOM/Zg computer program developed by the Faculty of Geodesy, University of Zagreb--Croatia, was used to analyze the signals measured with the geodetic equipment.  
Figures 5 and 6 show the frequency spectra of the response of the structure due to the induced vibration, which was measured with geodetic measuring equipment. The summary of the vibration measurement results is given in Table 2.  
Figure 7 on the left side shows a graph of vertical displacements as a result of geodetic measurement equipment, and Figure 7 on the right shows a graph of Peak Particle Velocity  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & & & \\ \hline \multicolumn{3}{c}{**Geodetic Measurement Equipment**} \\ \hline
**Measured Value** & **RTS TS50 (26 Hz)** & **RTS TS30** & **GNSS Topcon Hiper Pro** \\  & & **(6 Hz)** & **(10 Hz)** \\ \hline Vertical displacement (mm) & 5.9329 & 5.7000 & 27.00 \\ Lomb–Scargle & 29.8758 & 25.4003 & 39.8104 \\ A(f) (mm) & 1.4126 & 1.9863 & 2.8242 \\ Dominant frequency (Hz) & 2.5555 & 3.3116 & 0.0781 \\ Vertical amplitude (mm) & 0.5200 & 0.4046 & 4.8623 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Measured values obtained by geodetic methods.  
Figure 5: Lomb–Scargle periodogram for the frequency range between 0 and 1 Hz.  
Figure 6: The entire frequency spectrum of the Lomb–Scargle periodogram.  
Vertical (PPV V) obtained by analyzing the signals measured with a seismograph. The graphs show that the graphs are very similar in shape.  
Figure 8 shows the vibration velocities' Peak Particle Velocity in all three orthogonal directions--Transversal, Vertical and Longitudinal, measured by the seismograph.  
Figure 8: Peak Particle Velocity graph.  
Figure 7: Comparison between graphs of vertical displacement (**left**) and vibration velocity (PPV V) (**right**).  
The frequency spectrum of the signal over the entire measurement period in the vertical direction as a result of the FFT analysis is shown in Figure 9. The vertical axis shows the amplitude value, and the horizontal axis shows the frequency.  
A comparison of the frequency spectra obtained with surveying equipment and the values of relative displacements and velocities of vibration shows:  
The most important parameters are hereinafter described:  
* The graphs of the vertical displacements and the corresponding vibrational velocities in the vertical direction coincide and can also be compared only on the basis of graphs.
* Extreme value locations coincide relatively well.
* Phase graphs of vibration velocities and vertical displacements can be seen as a result of vibration excitation at different spans of the bridging structure.
* The dominant frequencies are generally relatively comparable.
* The amplitudes and measured displacements are generally incomparable.  
Table 3 shows the values of vertical displacements, dominant frequencies, and vertical amplitudes, which were calculated by analyzing the signals of the geodetic measuring equipment and the seismograph. We do not give the values of the data that were calculated by analyzing the signals of the Topcon Hiper Pro measuring equipment because they are not comparable due to the lack of precision of this equipment. Furthermore, the calculated displacement measured by the seismograph is not comparable as it represents the relative value of this quantity.  
Therefore, it can be concluded that the results of geodetic and physical measurements in the event under consideration were comparable from the standpoint of the corresponding graphical trajectories of the measured signals and the corresponding dominant frequencies obtained by spectral analysis.