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.

中文翻译：

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音频录音中电网频率的检测__从理论到实用检测器


最近，人们发现电网频率（ENF）可以通过数字音频、视频甚至图像文件捕获，并可以进一步用于法医调查。然而，多媒体内容中ENF的存在并不是确定的，如果ENF不存在，基于ENF的取证分析将变得毫无用处，甚至产生误导。在本文中，我们解决了数字音频录音中的 ENF 检测问题，该问题被建模为检测被未知有色宽感知平稳 (WSS) 高斯噪声污染的弱 (ENF) 信号，同时该信号还包含多个未知的随机参数。我们首先推导了三种Neyman-Pearson（NP）检测器，即通用匹配滤波器（GMF）、类匹配滤波器（MF）检测器和GMF的渐近逼近，并选择类MF检测器作为千里眼检测器。对于实际检测器，我们表明，由于未知噪声和大矩阵求逆，无法有效地获得广义似然比检验（GLRT）。或者，我们提出了两种基于最小二乘 (LS) 的时域检测器，称为 LS 似然比测试 (LRT) 和朴素 LRT。此外，我们提出了一种时频（TF）域检测器，称为 TF 检测器，它利用了 ENF 的先验知识。派生检测器的性能在测试统计分布、阈值选择和计算复杂度方面进行了广泛分析。研究发现，naive-LRT 探测器仅对非常短的记录有效。随着数据记录长度的增加，LS-LRT和TF检测器都能产生有效的检测结果，而后者近似于恒定虚警率（CFAR）检测器。 使用真实录音的实际实验证明了所提出的探测器和我们的分析的有效性。