# Noise Cancellation Method for Mud Pulse Telemetry Based on Discrete Fourier Transform
## 5 Conclusions  
In this study, we present the inherent properties of DFT, which provides an intuitive and concise representation of harmonic interference for MPT communication systems. By incorporating DFT, we significantly enhanced the communication performance of MPT systems. This integration allows for more precise identification and suppression of harmonic interference, which is a common issue in such communication channels. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{\
\begin{tabular}{c} **Modulation** \\ **Mode** \\ \end{tabular} } & \multirow{2}{*}{**Depth (m)**} & \multirow{2}{*}{
\begin{tabular}{c} **Data Rate** \\ **(bit/s)** \\ \end{tabular} } & \multicolumn{2}{c}{**BER**} & \multicolumn{2}{c}{**SIR (dB)**} \\ \cline{5-8}  & & & & **Traditional** & **DFT-Based** & **Traditional** & **DFT-Based** \\ \cline{1-1} \cline{5-8}  & & BFSK & 887 & 8 & 0 & 0 & 17.06 & 17.49 \\
2 & BFSK & 887 & 10 & 0.12 & 0.03 & 6.99 & 10.07 \\
3 & BFSK & 2559 & 12 & 0.11 & 0.05 & 7.39 & 10.72 \\
4 & BFSK & 2602 & 10 & 0.08 & 0 & 13.87 & 15.23 \\
5 & BFSK & 2632 & 6 & 0.19 & 0 & 7.89 & 12.48 \\
6 & BFSK & 2712 & 10 & 0.04 & 0 & 10.41 & 14.25 \\
7 & BFSK & 2890 & 10 & 0.14 & 0.12 & 6.59 & 8.19 \\
8 & BFSK & 3016 & 12 & 0.08 & 0 & 14.39 & 14.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of the two pumps’ noise cancellation methods. Additionally, the utilization of the FFT algorithm optimized the computational efficiency of our method, enabling real-time processing capabilities essential for practical applications. The effectiveness of our approach was validated using on-site pump noise. The simulation results consistently demonstrate a BER close to zero across various communication rates and modulation schemes, thereby confirming the robustness and reliability of the proposed interference elimination technique. Furthermore, we validated the effectiveness of our proposed method in experiments using communication data collected from real-world MPT environments, ensuring that our approach is not only theoretically sound but also practically viable. Future work will focus on expanding and refining our current methodology. Specifically, we intend to explore hybrid algorithms that integrate advanced signal processing techniques, such as wavelet transforms and VMD, to further enhance interference suppression capabilities. Additionally, we aim to investigate the adaptability of our method in more complex and dynamic interference environments, accommodating a broader spectrum of interference types and characteristics. These future endeavours will not only improve the performance and versatility of interference elimination in MPT systems but also contribute to the development of more reliable and efficient communication solutions applicable to a wide range of real-world scenarios. Conceptualization, [PERSON] ([PERSON]), Z.Z., and F.Q. ; methodology, [PERSON] ([PERSON]), Z.S., and J.Z. ([PERSON]); software, [PERSON] ([PERSON]), Z.Z., and Z.S. ; validation, [PERSON] ([PERSON]), Z.Z., and X.T. ; formal analysis, [PERSON] ([PERSON]), Z.S., [PERSON] ([PERSON]), and X.T. ; investigation, [PERSON] ([PERSON]), X.T., and Y.W. ; resources, [PERSON] ([PERSON]), X.T., and F.Q. ; data curation, Z.Z., X.T., and F.Q. ; writing--original draft preparation, [PERSON] ([PERSON]), [PERSON] ([PERSON]), and Z.S. ; writing--review and editing, [PERSON] ([PERSON]), X.T., Y.W., and F.Q. ; visualization, [PERSON] ([PERSON]), Z.Z., and Y.W. ; supervision, X.T., F.Q., and Y.W. ; project administration, Z.Z., X.T., and F.Q. ; funding acquisition, F.Q. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China for Zhejiang University, grant number 62101489. Not applicable. Data Availability Statement: Data are contained within the article. We express our thanks to [PERSON], [PERSON], [PERSON], and [PERSON] for their contributions to the field experiment. The authors declare no conflicts of interest.