Detection of Electric Network Frequency in Audio Recordings–From Theory to Practical Detectors

Recently, it has been discovered that the electric network frequency (ENF) could be captured by digital audio, video, or even image files, and could further be exploited in forensic investigations. However, the existence of the ENF in multimedia content is not a sure thing, and if the ENF is not present, ENF-based forensic analysis would become useless or even misleading. In this paper, we address the problem of ENF detection in digital audio recordings, which is modeled as the detection of a weak (ENF) signal contaminated by unknown colored wide-sense stationary (WSS) Gaussian noise, while the signal also contains multiple unknown random parameters. We first derive three Neyman-Pearson (NP) detectors, i.e., general matched filter (GMF), matched filter (MF)-like detector, and the asymptotic approximation of the GMF, and choose the MF-like detector as the clairvoyant detector. For practical detectors, we show that the generalized likelihood ratio test (GLRT) could not be efficiently obtained due to the unknown noise and large matrix inversion. Alternatively, we propose two least-squares (LS)-based time domain detectors termed as LS-likelihood ratio test (LRT) and naive-LRT. Further, we propose a time-frequency (TF) domain detector, termed as TF detector, which exploits the a priori knowledge of the ENF. The performances of the derived detectors are extensively analyzed in terms of test statistic distributions, threshold selection, and computational complexity. The naive-LRT detector is found to be only effective for very short recordings. As the data recording length increases, both LS-LRT and TF detectors yield effective detection results, while the latter is approximately a constant false alarm rate (CFAR) detector. Practical experiments using real audio recordings justify the effectiveness of the proposed detectors and our analysis.