# Application of Electrical Network Frequency of Digital Recordings for Location-Stamp Verification
## 2 Enf Extraction and Database Formation Based on Location Specific Recordings
### Classification Model  
Based on the extracted feature components, a multi-class SVM classification model is developed. In this work, radial basis function (RBF) kernel is used and the classification technique follows a \"one-versus-one\" approach. Algorithm 1 describes the training algorithm, whereas Algorithm 2 describes the testing algorithm. ```
1: Let \(X\) be the raw audio or power signal. The center frequency \(F_{c}\) of \(X\) is determined applying STFT. 2:\(X\) is classified as audio or power using SNR of the signal. 3: The ENF sequence is extracted from \(X\) applying Root MUSIC algorithm. The ENF sequence is divided into two segments--one is low outliers frequency (LOF) segment and another is high outliers frequency (HOF) segment. LOF is determined by passing the ENF sequence through a smoothening filter and HOF is determined by subtracting LOF from the original ENF sequence. 4: Feature vectors for both LOF and HOF segments based on the audio or power signal and its center frequency \(F_{c}\) are determined. 5: Each feature vector \(F_{p}\) is used in SVM classification algorithm as an input vector for training the prediction model. Table 7 presents the trained SVM models. Here the alphabets \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), \(G\), \(H\) and \(I\) denote the 9 grids used for training the SVM models. 14 SVM models are trained in total. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Features** & \(f_{50A_{1}}\) & \(f_{50A_{2}}\) & \(f_{50A_{3}}\) & \(f_{50A_{4}}\) \\ \hline \(f_{50A_{1}}\) & 0 & 54.03 & 0.09 & 11.89 \\ \(f_{50A_{2}}\) & 54.03 & 0 & 53.98 & 43.12 \\ \(f_{50A_{3}}\) & 0.09 & 53.98 & 0 & 11.82 \\ \(f_{50A_{4}}\) & 11.89 & 43.12 & 11.82 & 0 \\ \hline \end{tabular} \(f_{50A_{1}}\): Median. \(f_{50A_{2}}\): Modified Mean Absolute Value. \(f_{50A_{3}}\): 2 nd Coefficient \(G_{2}\) of AR(4) Model. \(f_{50A_{4}}\): Log of Variance of Auto Correlation Sequence.

\end{table} 
Table 6: Euclidean Distance Matrix Calculated for Selected Features (Table 2) for 50 Hz Audio ENF Signals. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Features** & \(f_{60A_{1}}\) & \(f_{60A_{2}}\) & \(f_{60A_{3}}\) & \(f_{60A_{4}}\) \\ \hline \(f_{60A_{1}}\) & 0 & 99.20 & 99.40 & \(1.51\times 10^{6}\) \\ \(f_{60A_{2}}\) & 99.20 & 0 & 0.24 & \(1.51\times 10^{6}\) \\ \(f_{60A_{3}}\) & 99.40 & 0.24 & 0 & \(1.51\times 10^{6}\) \\ \(f_{60A_{4}}\) & \(1.51\times 10^{6}\) & \(1.51\times 10^{6}\) & \(1.51\times 10^{6}\) & 0 \\ \hline \end{tabular} \(f_{60A_{1}}\): Log of Variance of Auto Correlation Sequence. \(f_{60A_{2}}\): Interquartile Range. \(f_{60A_{3}}\): Median. \(f_{60A_{4}}\): Power Spectral Density.

\end{table} 
Table 4: Euclidean Distance Matrix Calculated for Selected Features (Table 2) for 60 Hz Audio ENF Signals. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Features** & \(f_{50A_{1}}\) & \(f_{50A_{2}}\) & \(f_{50A_{3}}\) & \(f_{50A_{4}}\) \\ \hline \(f_{50A_{1}}\) & 0 & 54.03 & 0.09 & 11.89 \\ \(f_{50A_{2}}\) & 54.03 & 0 & 53.98 & 43.12 \\ \(f_{50A_{3}}\) & 0.09 & 5 However, for 50 Hz power dataset, there are six classes corresponding to six grids. Binary SVM classifier is applied in three ways to employ a multiclass classification method. Firstly, six classes are trained and tested following one versus all classification approach. Secondly, all possible combinations of the six classes are used taking two at a time. Then, all fifteen trained models are used for predicting new instances by means of the maximum vote as the decision making criterion. Both the techniques are implemented and the respective training and testing accuracies 50 Hz power and audio data are reported in Table 8. After experimenting with the fifteen trained models individually, it is found that classes \(B\), \(H\), \(E\), \(D\) and \(G\) are strongly separable from class \(F\). Therefore, five models named as \(BF\), \(HF\), \(EF\), \(DF\) and \(GF\) are used as a subset of the all fifteen trained models in a hierarchical structure to make the decision making system for 50 Hz power signals.