# Dynamic Matching of Reconstruction and Anti-Aliasing Filters in Adaptive Active Noise Control
## 5 Conclusions  
A dynamic matching method was proposed for the design of reconstruction and anti-aliasing filters in order to address the problems associated with group delay and high-frequency noise in systems with fixed reconstruction and anti-aliasing filters. The mirror noise and anti-aliasing noise evaluated in the digital regions at a high sampling rate are used to achieve the matching of digital reconstruction and anti-aliasing filters at a low sampling rate. Active noise control experiments were conducted in an anechoic chamber for primary sound sources with different spectral structures and different directions of incoming sound waves, and the experimental results demonstrated the following: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **ANR for “type a”** & **ANR for “type b”** & **ANR for “type c”** & **ANR for “type d”** \\
**Position (cm)** & **Method** & **(100 Hz–500 Hz)** & **(100 Hz–2000 Hz)** & **(100 Hz–2000 Hz)** & **(100 Hz–2000 Hz)** \\  & & **(dB)** & **(dB)** & **(dB)** & **(dB)** \\ \hline (192, 106) & Single-Rate Method & 2.1 & 0.2 & 0.2 & 0.2 \\ (192, 106) & Bai’s Method & 3.5 & 0.5 & 0.0 & \(-\)2.0 \\ (192, 106) & **Dynamic Matching Method** & **3.5** & **0.2** & **0.1** & **0.0** \\ (112, 166) & Single-Rate Method & 5.6 & 6.5 & 5.4 & 2.3 \\ (112, 166) & Bai’s Method & 12.2 & 14.2 & 6.4 & \(-\)2.5 \\ (112, 166) & **Dynamic Matching Method** & **10.9** & **12.4** & **12.1** & **10.8** \\ (0, 250) & Single-Rate Method & 12.8 & 13.8 & 13.6 & 11.2 \\ (0, 250) & **Bai’s Method** & 13.0 & 13.2 & 7.8 & \(-\)5.3 \\ (0, 250) & **Dynamic Matching Method** & **13.2** & **14.6** & **14.3** & **12.6** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of ANR values for different positions and methods. 1. The reconstruction filter directly affected the mirror noise exported by the ANC system, and primary sound sources with different spectral structures had different requirements for the attenuation characteristics of the reconstruction filter;
2. For primary sound sources with weak low-frequency components, anti-aliasing filters with slow roll-off rate can be used; however, when high-frequency components become significant, such anti-aliasing filters may limit the noise reduction of ANC and even cause low-frequency uplift;
3. Increasing the roll-off rate of reconstruction and anti-aliasing filters is often not the best choice as these two types of filters will bring additional group delays to the system; therefore, one needs to consider a trade-off between the suppression of high-frequency noise and the group delay for practical systems;
4. The proposed method can significantly improve the noise reduction performance of the ANC system while effectively suppressing the mirror noise and aliasing noise. Future research will extend these results to the typical ANC applications mentioned in the introduction, especially for the scenes with directional primary sources. Furthermore, an investigation into the effect of methods combining the proposed method and beamforming technology in an ANC system will be conducted. Conceptualization, F.Z. and X.L. ; Data curation, F.Z., [PERSON] ([PERSON]), and [PERSON] ([PERSON]); Formal analysis, F.Z. ; Funding acquisition, X.L. ; Methodology, F.Z. ; Project administration, X.L. ; Resources, X.L. ; Software, F.Z. ; Supervision, [PERSON] ([PERSON]); Validation, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); Visualization, F.Z. ; Writing--original draft, F.Z. ; Writing--review and editing, [PERSON] ([PERSON]), [PERSON] ([PERSON]), and X.L. All authors have read and agreed to the published version of the manuscript. All authors will be informed about each step of manuscript processing, including submission, revision, revision reminders, etc., via emails from our system or assigned Assistant Editor. This research was funded by National Key R&D Program of China under Grant 2023 QY0803.