Electric network frequency (ENF) modeling, which aims to use mathematical models to describe its random fluctuation properties and establish feature extraction, statistical analysis, and trajectory prediction capabilities, has been an important research subtopic in ENF-based digital forensics. In this paper, we first illustrate the limitations of the existing autoregressive (AR) model and then conduct a comprehensive statistical analysis based on practically recorded ENF data from Central China Grid. Specifically, we apply the autoregressive integrated moving average model (ARIMA) and two Markov chain based models respectively in ENF modeling for solving corresponding model parameters. Through the comparative analysis, we reveal that the ARMA(2,4) model is theoretically the best choice for ENF modeling, whereas with the consideration of the frequency resolution limitation in practical situations, the Markov chain model is more suitable to model the estimated ENF from a testing file.
WANG Qingyi, HUA Guang, ZHANG Haijian
. Electric Network Frequency Modeling for Multimedia Forensics[J]. Journal of Applied Sciences, 2022
, 40(3)
: 477
-492
.
DOI: 10.3969/j.issn.0255-8297.2022.03.011
[1] 杨锐,骆伟祺,黄继武.多媒体取证[J].中国科学:信息科学, 2013(12):1654-1672. Yang R, Luo W Q, Huang J W. Multimedia forensics[J]. SCIENTIA SINICA Informationis, 2013, 43(12):1654-1672.(in Chinese)
[2] 付剑晶,陈德人,徐达文,等.适用于双重压缩环境的图像内容认证水印算法[J].中国科学:信息科学, 2019, 49(4):100-121. Fu J J, Chen D R, Xu D W, et al. A watermarking algorithm for image content authentication in double-compression environment[J]. SCIENTIA SINICA Informationis, 2019, 49(4):100-121.(in Chinese)
[3] Lawgely A, Khelifi F. Sensor pattern noise estimation based on improved locally adaptive DCT filtering and weighted averaging for source camera identification and verification[J]. IEEE Transactions on Information Forensics and Security, 2017, 12(2):392-404.
[4] Malik H. Acoustic environment identification and its applications to audio forensics[J]. IEEE Transactions on Information Forensics and Security, 2013, 8(11):1827-1837.
[5] 中国国家标准化管理委员会.《电能质量电力系统频率偏差》:GB/T15945-2008[S]. 2008.
[6] Cooper A J. An automated approach to the electric network frequency (ENF) criterion-theory and practice[J]. Forensic Linguistics, 2009, 16(2):193-218.
[7] 李明德,夏向阳,王锦泷,等.基于分布式电源的电网电压和频率控制优化[J].中国电力, 2016(4):166-169. Li M D, Xia X Y, Wang J L, et al. Voltage and frequency control optimization for distributed generation based grid[J]. Electric Power, 2016(4):166-169.(in Chinese)
[8] Zheng L, Zhang Y, Lee C E, et al. Time-of-recording estimation for audio recordings[J]. Digital Investigation, 2017, 22:S115-S126.
[9] Kajstura M, Trawinska A, Hebenstreit J. Application of the electrical network frequency (ENF) criterion:a case of a digital recording[J]. Forensic Science International, 2005, 155(2/3):165-171.
[10] Elmesalawy M M, Eissa M M. New forensic ENF reference database for media recording authentication based on harmony search technique using GIS and wide area frequency measurements IEEE Transactions on Information Forensics and Security, 2014, 9(4):633-644.
[11] Hua G, Goh J, Thing V L L. A dynamic matching algorithm for audio timestamp identification using the ENF criterion[J]. IEEE Transactions on Information Forensics and Security, 2014, 9(7):1045-1055.
[12] Hua G. Error analysis of forensic ENF matching[C]//2018 IEEE International Workshop on Information Forensics and Security (WIFS), 2018:1-7.
[13] 崔三帅,毛毛雨,林晓丹,等.图像视频中ENF信号的分析及应用综述[J].应用科学学报, 2019, 37(5):573-589. Cui S S, Mao M Y, Lin X D, et al. Survey on analysis and applications of electric network frequency (ENF) signals in image and video[J]. Journal of Applied Sciences, 2019, 37(5):573-589.(in Chinese)
[14] Esquef P A A, Apolinario J A, Biscainho L W P. Edit detection in speech recordings via instantaneous electric network frequency variations[J]. IEEE Transactions on Information Forensics and Security, 2014, 9(12):2314-2326.
[15] Hua G, Zhang Y, Goh J, et al. Audio authentication by exploring the absolute-error-map of ENF signals[J]. IEEE Transactions on Information Forensics and Security, 2016, 11(5):1003-1016.
[16] Reis P M G I, Costa J P C L D, Miranda R K, et al. Esprit-Hilbert-based audio tampering detection with SVM classifier for forensic analysis via electrical network frequency[J]. IEEE Transactions on Information Forensics and Security, 2017, 12(4):853-864.
[17] Hajj-Ahmad A, Garg R, Wu M. ENF-based region-of-recording identification for media signals[J]. IEEE Transactions on Information Forensics and Security, 2015, 10(6):1125-1136.
[18] Yao W, Zhao J, Till M, et al. Source location identification of distribution-level electric network frequency signals at multiple geographic scales[J]. IEEE Access, 2017:11166-11175.
[19] Wong C W, Hajj-Ahmad A, Wu M. Invisible Geo-location signature in a single image[C]//2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2018:1987-1991.
[20] Grigoras C. Digital audio recordings analysis:the electric network frequency (ENF) criterion[J]. International Journal of Speech Language and the Law, 2005, 12(1):63-76.
[21] Garg R, Varna A L, Wu M. Modeling and analysis of electric network frequency signal for timestamp verification[C]//2012 IEEE International Workshop on Information Forensics and Security (WIFS), 2012:67-72.
[22] Hajj-Ahmad A, Garg R, Wu M. Instantaneous frequency estimation and localization for ENF signals[C]//Signal&Information Processing Association Summit&Conference, 2013:1-10.
[23] Pemberton J. Time series analysis with applications in R, second edition[J]. Journal of Applied Statistics, 2011, 38(5/6):1311-1312.
