Electrical network frequency (ENF) maximum-likelihood estimation via a multitone harmonic model

Estimation of the parameters of the electric network signal, usually present in many audio and video recordings, is known to have several important forensic applications. In this paper, we consider the problem of estimating the base frequency and signal to noise ratio (SNR). Although the electric network signal is present via its base frequency and its integer multiplies, recent estimators in the literature focus on single-tone models. In this work, we offer a multitone harmonic model for the electric network signal. We use the Cramer-Rao bound for the frequency estimation problem and show that this approach can lead to a theoretical $O(M^{3})$ factor improvement in the estimation accuracy, where $M$ is the number of harmonics. We then derive the computationally efficient form of the maximum-likelihood estimator, applicable in the limit of large number of measurements. The problem of estimating the SNR of the signal is also discussed. Through extensive tests on real data and data sets reported in the current literature, the performance of the new estimators is evaluated. Results indeed show a significant gain compared to the single-tone model, and are better than previously reported estimators in the literature for moderate and high SNR values.