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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录音中电网频率的检测-从理论到实际检测器

最近，已经发现，电网频率（ENF）可以被数字音频，视频甚至图像文件捕获，并且可以进一步用于法医调查中。但是，不确定ENF是否存在于多媒体内容中，并且如果ENF不存在，则基于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彩色宽广平稳（WSS）高斯噪声污染的弱（ENF）信号，而该信号还包含多个未知信号随机参数。我们首先导出三个Neyman-Pearson（NP）检测器，即通用匹配滤波器（GMF），类匹配滤波器（MF）的检测器以及GMF的渐近逼近，并选择类似MF的探测器作为透视探测器。对于实际的检测器，我们表明由于未知噪声和大矩阵求逆，无法有效获得广义似然比测试（GLRT）。另外，我们提出了两个基于最小二乘（LS）的时域检测器，分别称为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。从测试统计量分布，阈值选择和计算复杂性方面广泛分析了派生检测器的性能。发现朴素的LRT检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检测器都会产生有效的检测结果，后者大约是恒定的误报率（CFAR）检测器。使用实际音频记录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。