Robust Electric Network Frequency Estimation with Rank Reduction and Linear Prediction

Abstract

This article deals with the problem of Electric Network Frequency (ENF) estimation where Signal to Noise Ratio (SNR) is an essential challenge. By exploiting the low-rank structure of the ENF signal from the audio spectrogram, we propose an approach based on robust principle component analysis to get rid of the interference from speech contents and some of the background noise, which in our case can be regarded as sparse in nature. Weighted linear prediction is enforced on the low-rank signal subspace to gain accurate ENF estimation. The performance of the proposed scheme is analyzed and evaluated as a function of SNR, and the Cramér-Rao Lower Bound (CRLB) is approached at an SNR level above -10 dB. Experiments on real datasets have demonstrated the advantages of the proposed method over state-of-the-art work in terms of estimation accuracy. Specifically, the proposed scheme can effectively capture the ENF fluctuations along the time axis using small numbers of signal observations while preserving sufficient frequency precision.

Efficient Capon-Based Approach Exploiting Temporal Windowing for Electric Network Frequency Estimation

“…3 a correlation coefficient of 0.9990 is obtained, when a frame length of 20 seconds is employed. This value exceeds the state-of-the-art linear prediction estimation presented in [7], which reaches 0.9984 even though their value is not purely from the linear prediction method due to the fact that there has been made a denoising procedure before. Moreover, the aforementioned value of 0.9990 overcomes the Maximum Likelihood (ML) method and the Welch one, which was properly parametrized in [8].…”

“…Additionally, it is demonstrated that longer frame lengths do not necessarily imply better accuracy in terms of correlation coefficient. [4] 0.8826 0.9852 0.9953 0.9977 Linear Prediction [7] 0.9651 0.9959 0.9976 0.9984 Welch [8] 0.9847 0.9989 0.9989 0.9983 Weighted Spectrogram [7] 0.8255 0.9873 0.9944 0.9966 The second dataset (Data 2) comprises of speech recordings in which interference exist and suffers from low SNR. In Data 2, we studied the second harmonic, where a higher SNR permits us to obtain reliable results.…”

Blackman–Tukey spectral estimation and electric network frequency matching from power mains and speech recordings

“…The proposed approach BT + LWD outperforms in terms of mSDE the TRIAA (Track) and demonstrates statistically significant improvements compared to the conventional BT method. The state‐of‐the‐art methods proposed in [35] did not provide results regarding mSDE. To conclude, BT + LWD was found to be the top‐performing approach for ENF estimation in the first and second harmonics and the second best approach for ENF estimation in the third harmonic with respect to mSDE.…”

“…Specifically, the range of pitch frequencies is approximately 120–350 Hz and 100–200 Hz for females and males, respectively [66]. The proposed BT + LWD delivered an MCC value of 0.9434, outperforming the recent state‐of‐the‐art approach in ENF estimation, that is, linear prediction, [35], which yields an MCC of 0.9366. Moreover, the proposed approach also outperforms TRIAA, which yields an MCC value of 0.9305.…”

“…Interference in speech signals hinders ENF estimation. To cope with that problem, robust principal component analysis was employed for noise reduction and weighted linear prediction for ENF estimation was introduced in [35]. Fine tuning of signal filtering and parametrisation for ENF estimation in recordings from power mains and speech recordings can increase ENF estimation accuracy.…”