## 3 Results  
The dataset that is created, as per the discussion in Section 3, is for the training and testing of DNN models. Statistical features of all ZCP datasets, which are Dataset-1: noise levels 10% to 50%, Dataset-2: THD levels 10% to 50%, Dataset-3: noise levels 10% to 40% with THD level 50% and Dataset-4: Noise levels 5% to 20%, have been used to train the DNN model presented in Tables 2-5 respectively. The back-propagation through time (BPTT) algorithm with the Adam optimizer is used to train the proposed DNN model. The proposed DNN model is being implemented and tested in Google Colab. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **F1: Intercept** & **F2: Slope** & **F3: Correlation** & **F4: RMSE** \\ \hline count & 3948 & 3948 & 3948 & 3948 \\ mean & 7.9240602 & \(-155.89604\) & 0.515395084 & 13.2242 \\ std & 375.9320982 & 6605.02961 & 0.523116944 & 4.916469 \\ min & \(-1123.05498\) & \(-14989.989\) & \(-0.939147665\) & 5.080782 \\
25\% & \(-167.2859958\) & \(-5086.192\) & 0.238110698 & 10.42127 \\
50\% & 9.096503124 & \(-186.74614\) & 0.7423585 & 11.35477 \\
75\% & 176.4562648 & 4785.236 & 0.924238256 & 16.65624 \\ max & 1308.768218 & 15297.0099 & 0.999727701 & 25.40568 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical information of ZCP dataset with THD level 50% and noise level from 10% to 40%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **F1: Intercept** & **F2: Slope** & **F3: Correlation** & **F4: RMSE** \\ \hline count & 4935 & 4935 & 4935 & 4935 \\ mean & 0.906008423 & \(-18.676729\) & 0.494900872 & 2.54591076 \\ std & 84.85917791 & 1464.64472 & 0.367675132 & 3.23948602 \\ min & \(-381.4180671\) & \(-4065.341\) & \(-0.816551207\) & 0.02172266 \\
25\% & \(-16.76426941\) & \(-350.0215\) & 0.217181932 & 0.21942497 \\
50\% & 0.891192436 & \(-11.922465\) & 0.54121887 & 0.40202541 \\
75\% & 18.56990887 & 341.755478 & 0.820813532 & 5.27377613 \\ max & 343.7762144 & 4706.99757 & 0.999293572 & 10.5857103 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical information of ZCP dataset with noise level from 10% to 50%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **F1: Intercept** & **F2: Slope** & **F3: Correlation** & **F4: RMSE** \\ \hline count & 4435 & 4435 & 4435 & 4435 \\ mean & \(-0.280990216\) & \(1.57238\times 10^{-5}\) & 0.595490707 & 0.211104753 \\ std & 197.2465139 & \(383.2663092\) & 0.686412231 & 0.102681968 \\ min & \(-79.60710789\) & \(-995.088821\) & \(-0.995488795\) & 0.059104012 \\
25\% & \(-9.873091003\) & \(-261.7826384\) & 0.638777912 & 0.128286631 \\
50\% & 0.336220664 & 0.000110454 & 0.974343224 & 0.212132057 \\
75\% & 9.320462957 & 261.7824332 & 0.99412752 & 0.29862303 \\ max & 69.65621941 & 995.088821 & 0.999831274 & 0.403321083 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical information of ZCP dataset with THD level from 10% to 50%. Box plots are used to identify the outliers against each input feature in every dataset mentioned above. Box plots against each feature for Dataset-1, Dataset-2, Dataset-3 and Dataset-4 are shown in Figures 7-10, respectively. From all these plots, it has been observed that features in all datasets, such as intercept, correlation and slope, have outliers as data exist below the 25% interquartile range and above the 75% interquartile range. These outliers are due to spikes in distorted signals due to noise and harmonics and cannot be removed from data to make the model predict zero-crossing points under noise and harmonics. Figure 8: Box plot for each input feature in Dataset-2 (THD level from 10% to 50%) **(a)** m. (b) c. (c) R. **(d)** RMSE. Figure 9: Box plot for each input feature in Dataset-3 (noise level from 10% to 40% and THD level 50%). **(a)** m. (b) c. (c) R. **(d)** RMSE.