# Application of Electrical Network Frequency of Digital Recordings for Location-Stamp Verification
## 2 Enf Extraction and Database Formation Based on Location Specific Recordings
### Analysis of Extracted Feature Vectors  
Statistics and signal processing techniques are applied to extract potential feature vectors from the ENF sequences. Table 2 presents the extracted feature vectors from the HOF and LOF segments of 60 Hz and 50 Hz power and audio ENF signals. From analysis, mean and median are proved to be good candidates for potential feature functions. Waveform length is another good candidate to extract a potential feature vector \(F_{v,wl}\), which is measured as  
\[F_{v,wl}=\sum_{i=1}^{N-1}|f[i+1]-f[i]| \tag{2}\]  
Here \(f[\cdot]\) is an ENF sequence and \(N\) is the sequence length. \begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{3}{c}{**Power**} & \multicolumn{3}{c}{**Audio**} \\ \hline \(\mathbf{F_{c}=60\) Hz} & \(\mathbf{F_{c}=50\) Hz} & \(\mathbf{F_{c}=60\) Hz} & \(\mathbf{F_{c}=50\) Hz} \\ \hline
**HOF** & **LOF** & **HOF** & **LOF** & **HOF** \\ \hline
1. Waveform Length & 1. Mean & 1. 2 nd Coefficient \(G_{2}\) of AR(4) Model & 1. Log of Variance of Auto Correlation Sequence & 1. Median \\ \hline
2. Log of Variance of Auto Correlation Sequence & 2. Waveform Length & - & 2. Interquartile  Range & 2. Modified Mean Absolute Value \\ \hline
3. Log of Final Prediction Error \(H\) of AR(4) Model & 3. Median & - & 3. Median & 3. 2 nd Coefficient \(G_{2}\) of AR(4) Model \\ \hline - & 4. Crest Factor & - & 4. Power Spectral Density & 4. Log of Variance of Auto Correlation Sequence \\ \hline - & 5. Interquartile Range & - & - & - \\ \hline \end{tabular}
\end{table} 
Table 2: Extracted Feature Vectors from the high outliers frequency (HOF) and low outliers frequency (LOF) Segments of the Original 60 Hz and 50 Hz ENF Sequences. However, from analysis, crest factor (CF) and interquartile range (IQR) are found to be potential feature functions. For an ENF signal, CF is measured as the ratio of the peak value to the root mean square (rms) value. IQR refers to the difference between the ENF value below which lie 25% of the entire sequence data and that below which lie 75% of the entire sequence data. IQR analyzes the ENF sequence in terms of quartiles. Quartiles divide the data into four equal parts. The values that divide each part are called the first (\(Q_{1}\)), second (\(Q_{2}\)) and third (\(Q_{3}\)) quartiles. \(Q_{1}\) is the middle value of the first half of the sequence. \(Q_{2}\) is the median value and \(Q_{3}\) is the middle value of the second half of the sequence. IQR is equal to \(Q_{3}-Q_{1}\). Another potential feature vector \(F_{v,ma}\) is derived from the modified mean absolute value function. It is defined as  
\[F_{v,ma}=\frac{\sum\limits_{i=1}^{N}0.5|f[i]|}{N} \tag{3}\]  
Welch power spectrum method is used to measure the power spectral density of an ENF sequence, which is proved to be a good feature component. However, 4 th order autoregressive AR(4) model of an ENF sequence can be expressed as  
\[f[n]=G_{1}f[n-1]+G_{2}f[n-2]+G_{3}f[n-3]+G_{4}f[n-4]+H \tag{4}\]  
Here \(G_{1}\)-\(G_{4}\) are the AR coefficients and \(H\) is the final prediction error (the variance estimate of the white noise input to the AR model). In this work, AR parameters are estimated using Burg method, where \(G_{2}\) and log of \(H\) are analyzed as potential feature vectors. However, no potential feature component is extracted from LOF 50 Hz power, HOF 60 Hz audio and LOF 50 Hz audio ENF segments. Experiments are conducted for extracting feature vectors from the ENF signals. Then the most promising candidates for final features are selected by analyzing the Euclidean distance between each pair of features. The higher distance value of a particular feature from other features makes it a better feature to be selected. The concept and properties of Euclidean distance matrices are reported in Reference [24]. The Euclidean distance matrices of the selected features for 60 Hz power, 60 Hz audio, 50 Hz power and 50 Hz audio ENF sequences are presented in Tables 3-6 respectively.