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Frequency is an important parameter for the operation and control of power systems. One novel application of frequency measurements involves using this information to authenticate a digital audio/video recording presented as forensic evidence in legal proceedings. To apply this technique, called the electrical network frequency (ENF) criterion, both a reference frequency database and an accurate frequency estimation method are required. This paper briefly introduces a wide-area frequency monitoring network (FNET) as the reference frequency database and analyzes statistical features of frequency of the four North American interconnections in terms of different time scales. Combined with digital filtering and a three-sample interpolation, the short-time Fourier transform (STFT) is adjusted to estimate the ENF embedded in digital audio recordings. A procedure of using the ENF criterion, ranging from signal preprocessing to ENF estimation and reference frequency database matching, is then proposed. Further, oscillator error of the digital recording device is considered and an iterative error correction method is given to assist with the frequency database matching. Factors which influence the accuracy of frequency estimation, such as parameter selections of the STFT and signal-to-noise ratio, are also discussed. Test results show that the procedure is capable of performing digital audio authentication.