## 3 Theoretical Analysis
### Algorithm Flow
\begin{table}
\begin{tabular}{c c c c c} \hline
**Before Denoising** & **Amplitude** & **Frequency** & **Phase\({}^{\circ}\)** & **Amplitude, Frequency and Phase Errors/\%** \\ \hline \multirow{4}{*}{5 dB} & 50.2379 & 49.9946 & 71.7320 & 0.3216/0.0108/0.3722 \\  & 24.8951 & 149.9963 & 107.1586 & 0.4196/0.0025/0.7791 \\  & 8.7083 & 137.8659 & 141.9504 & 2.4506/0.0972/1.4233 \\  & 6.1268 & 349.9532 & 160.7258 & 1.1806/0.0134/0.3282 \\ \hline \multirow{4}{*}{10 dB} & 50.4065 & 49.9963 & 72.3137 & 0.0129/0.0074/0.4357 \\  & 25.1007 & 150.0043 & 107.9841 & 0.4028/0.0029/0.0147 \\  & 8.6343 & 137.9901 & 143.9876 & 1.5800/0.0072/0.0086 \\  & 6.2607 & 350.0049 & 160.4478 & 0.9790/0.0014/0.1547 \\ \hline \multirow{4}{*}{20 dB} & 50.3869 & 49.9994 & 72.0592 & 0.0260/0.0012/0.0822 \\  & 25.0419 & 149.9997 & 108.0167 & 0.1676/0.0002/0.0155 \\  & 8.5718 & 138.0054 & 143.8190 & 0.8447/0.0039/0.1257 \\  & 6.3054 & 350.0015 & 160.4092 & 1.7000/0.0004/0.1306 \\ \hline \multirow{4}{*}{30 dB} & 50.3943 & 49.9998 & 72.0175 & 0.0113/0.0004/0.0243 \\  & 24.9830 & 150.0001 & 107.9953 & 0.0680/0.0001/0.0044 \\  & 8.4957 & 137.9972 & 144.1354 & 0.0506/0.0020/0.0940 \\  & 6.2310 & 350.0006 & 160.1573 & 0.5000/0.0002/0.0267 \\ \hline \end{tabular}
\end{table} 
Table 2: Detection results and errors of harmonic signals by the proposed method. racy in fitting noise signals. The amplitude of the false component in the fitting result of the Prony algorithm is much smaller than that of the non-false component. According to the dominant factor, non-false components are accurately screened out and all fundamental, harmonic and interharmonic components are successfully detected. Hence, it is experimentally verified that the proposed method possesses remarkable robustness and adaptability under different noise intensities of electric energy signals. Its detection of harmonics and interharmonics is accurate, stable and reliable, which implies that the method is well-suited for the detection of harmonics and interharmonics in power systems under various noise environments. Finally, compared to the particularly high accuracy of the proposed method for frequency detection in signals, there is still room for improvement in terms of the detection accuracy of amplitude and phase. In the future, it is worthwhile to incorporate neural networks in the current method for higher detection accuracy for amplitude and phase. Conceptualization, S.L. ; Methodology, J.G. and S.L. ; Validation, J.G. ; Resources, S.L. ; Data curation, J.G. ; Writing--original draft, J.G. ; Writing--review & editing, S.L. All authors have read and agreed to the published version of the manuscript. This research was supported by Professor [PERSON]'s National Natural Science Foundation of China (61961016), Hubei Provincial Natural Science Foundation (2019 CFB9593), and Hubei University for Nationalities Doctoral Research Initiation Fund (MY2018B08). This research does not require ethical approval. Not applicable. Choosing not to disclose data due to privacy reasons. The authors declare no conflict of interest. ## References

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