## 4 Experiments
### Half of Frequencies vs. Quarter of Frequencies  
CVNN excels a real-valued one but inevitably doubles the training parameters due to the extra complex part. However, since the input signal is a real value, only half of the frequencies have the meaning, and no additional information is carried by the other half because of conjugate symmetry. That is to say, \(X_{k}=X_{120-k}^{*}\) as for FFT results \(\{X_{k}\}_{k=0}^{119}\) except for direct-current (DC) component \(X_{0}\) and symmetry axis \(X_{60}\). To this end, we use only half of frequencies \(X_{0}\sim X_{60}\), which is enough to represent the whole information of the frequency domain. As can be seen in Figure 3 and Table 1, there is not a great deal of difference between them, which indicates that the additional training parameters introduced by the complex part can be reduced for real input.  
Additionally, we make another attempt to further narrow the frequency range by only using low-frequency components of FFT results. Since we do not conduct a frequency shift (FFtshift), the low-frequency components lie on the far left (\(X_{0}\sim X_{30}\)) and far right (\(X_{90}\sim X_{119}\)) of the frequency band, and we choose the former as explained before. As a result in the second last column and row in Figure 3 and Table 1, we surprisingly find that a further reduction of parameters does not bring about a drop in performance; conversely, it outperforms the results from using half of the frequencies and full frequencies by 2.94% and 1.19% in terms of recall rate and F1 score despite a 0.78% loss in accuracy. It may be attributed to the fact that neural networks prefer low-frequency components while selectively ignoring high-frequency ones; thus, pure low-frequency input without interference from noise in high-frequency components will lead to better outcomes. To make it more convincing, we also conduct comparison experiments by using pure high-frequency components (\(X_{31}\sim X_{60}\)). As might have been expected, it turns out to be a mess  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Accuracy** & **Recall Rate** & **F1 Score** \\ \hline RVNN & 90.99\% & 83.21\% & 86.92\% \\ CVNN & 94.89\% & 82.48\% & 88.25\% \\ CVNN(\(X_{0-60}\)) & 94.49\% & 82.97\% & 88.36\% \\ CVNN(\(X_{0-30}\)) & 93.71\% & 85.73\% & 89.55\% \\ CVNN(\(X_{31\sim 60}\)) & 72.75\% & 64.83\% & 68.56\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Quantitative comparison results between different models in terms of accuracy, recall rate and F1 score. The best and poorest performance for each metric is marked as pink and light gray signs, respectively.  
Figure 3: Comparison results between RVNN and CVNN as well as several variations for CVNN. \(X_{0\sim 60}\), \(X_{0\sim 30}\) and \(X_{31\sim 60}\) represent the only use of the first half, first quarter (low-frequency) and second quarter (high-frequency) of frequency components, respectively.  
with much noise reflected on qualitative results in the last column in Figure 3. We can also clearly see from the last two rows in Table 1 that it has the poorest performance on all metrics, which again proves that the low-frequency part plays a leading role in the training of the neural network whereas the high-frequency part will disturb it.