# Data Fusion of Multivariate Time Series: Application to Noisy 12-Lead ECG Signals
## 4 Application of NDFA in 12-Lead ECG Signals
### Synthetic Signals Experiments
#### 4.1.2 Noise Contaminated Synthetic Signals Experiments  
In this subsection, the trajectory fusion problem of the noisy VCG signals will be discussed. To ensure the objectivity of experiment in this study, realistic noises were adopted from NSTDB and the three types of realistic noise, baseline wander (BW), electrode movement (EM), and muscle artifact (MA) are shown in Figure 5, respectively.  
Figure 4: Reconstructed phase trajectories of synthetic ECG signals. (**a–c**) are reconstructed phase trajectories of \(V_{x}\), \(V_{y}\) and \(V_{z}\), respectively. (**d**) Is reconstructed phase trajectory of final fused result via NDFA.  
To further illustrate the validity of NDFA, the three types of noise, BW, EM and MA, were added to clean synthetic VCG signals with different magnitudes of signal noise ratio (SNR). Twelve-lead ECG signals were transformed to 3-lead VCG signals by linear transformation. It means that the signal quality of 12-lead ECG was inherited to some degree. In other words, if one lead signal in 12-lead ECG signals is contaminated by noise, the quality characteristics of the lead signal will also be reflected in the VCG signals. In the experiment, the lead \(V_{x}\) of VCG signals is randomly chosen, which is contaminated by the noise. The parameters of the SNR levels are summarized in Table 3[11].  
Here the lead \(V_{x}\) is polluted by BW and the magnitudes of SNR are 12 dB, 6 dB, 0 dB, and \(-6\) dB, respectively. In Table 4, correlation coefficient \(Cor_{\overline{x}}\) is the mean value of \(Cor(Vx,Vy)\) and \(Cor(Vx,Vz)\). The parameter \(Cor_{\overline{x}}\) is the mean value of \(Cor(s,Vx)\), \(Cor(s,Vy)\), and \(Cor(s,Vz)\). The values of parameters \(Cor_{\overline{x}}\) and \(Cor_{\overline{y}}\) reflect the degree of correlations between the original and fused signals. From Table 4, we can find that, under the different SNR levels, the correlation coefficient \(Cor_{\overline{y}}\) is greater than \(Cor_{\overline{x}}\) consistently, thereby designating the effectiveness of NDFA.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SNR (dB)** & **12** & **6** & **0** & \(\mathbf{-6}\) \\ \hline \(Cor_{\overline{x}}\) & 0.3449 & 0.3103 & 0.2340 & 0.1368 \\ \(Cor_{\overline{x}}\) & 0.5369 & 0.5329 & 0.5177 & 0.4566 \\ \hline \hline \end{tabular}
\end{table}
Table 4: \(Cor\) for BW with different signal noise ratio (SNR) levels.  
Figure 5: Realistic noise signals.  
Analogously, here the clean \(V_{x}\) signal is polluted by the noise of EM and MA with different magnitudes of SNR and the correlations coefficients are calculated in Tables 5 and 6. In the two tables, the relations between noisy signals and fused results are highly consistent with the relation reflected in Table 4.  
With the experimental results being comprehensively analyzed under different conditions, it suggests that with NDFA being employed, the reconstructed trajectories of fused results can effectively describe the quality characteristics of noisy synthetic ECG signals. In order to test the performance of our method adequately, some realistic ECG signals will be applied in Section 4.2.