The electric network frequency (ENF) in the US has a nominal value of f = 60 Hz and its instantaneous value fluctuates r

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The Electric Network Frequency Enf In The Us Has A Nominal Value Of F 60 Hz And Its Instantaneous Value Fluctuates R 1 (281.52 KiB) Viewed 25 times

The electric network frequency (ENF) in the US has a nominal value of f = 60 Hz and its instantaneous value fluctuates round the nominal value as a function of time [1]. The following plots show some sample ENF signals from various power grids [2]. 508 50.6 50.41 50.21 608 60.6 00.4 60.21 en $ 60 59.8 59.6 59.4 59.26 60.84 60.6 604 60.4 60 2 601 59.6 59.B 59.4 50.8 50.6 504 50.2 1950 50 49.8 496 49.4 al ) 249.84 49.6 49.4 592 49 2000 4000 6000 8000 10000 2000 8000 10000 2000 8000 10000 4000 8000 time (sec) 4000 6000 time (sec) 2000 8000 time (sec) 10000 4000 G000 time (sec) US East Texas Ireland Lebanon The ENF signals can be captured by audio or video recordings made in areas where there is electrical activity. This makes the ENF a good criterion for the forensic analysis of a multimedia recording. With a proper reference database, one can tell when and where a recording was made, and whether the recording has been tampered. = Let us formally define the ENF signal as f(t) = fo + u(t), where f, is the nominal value and u(t) is the random, fluctuating component. Research found that the random signal u(t) can be modeled as an autoregressive (AR) random process [1]. In this project, we assume that its sampled version (with a discretization step size of 0.2 seconds) follows the first-order AR process, namely, u[n] = 0.9u[n 1] + e[n], where the e[n] is a zero-mean white Gaussian noise process with standard deviation ax = 0.05 Hz. Note that the discretization leads to the relationship of n=t/ 0.2, and the discretized ENF signal can still be decomposed into f[n] = fo+ u[n]. A realization of a white Gaussian process of length L with standard deviation of q can be obtained by using the q*randn(1, 1) command. To generate a random process u[n], you may assume u[0] = 0 and use a for loop to iteratively generate u[1], u[2], ... (a) [Simulate ENF Signals] Generate 5 different discrete ENF signals of 10 minutes long each and plot them in the same figure. Limit the dynamic range of the vertical axis to around 60 Hz (e.g., 59.6 to 60.4 Hz) to ensure that the fluctuation can be easily observed. Label the horizontal axis in the unit of minute. Use different color for different ENF signals.