# Dynamic Matching of Reconstruction and Anti-Aliasing Filters in Adaptive Active Noise Control
## 4 Experimental Validation
### Experimental Process and Results  
Four types of primary sound sources were used in the experiment. The first type (marked \"type a\") was band-limited white noise, with the highest frequency being below 500 Hz; the second (marked \"type b\") and the third (marked \"type c\") were also white noise, but with the highest frequencies being 2000 Hz and 5000 Hz, respectively. The last type of primary noise, \"type d\", was a special primary noise that we constructed; the frequency components from 2000 Hz to 5000 Hz were raised unequally, and the frequency components below 2000 Hz were weakened unequally. The acoustic power levels emitted by the primary sound source of these four types were about 84 dB, 91 dB, 95 dB, and 93 dB, respectively. The whole ANC process included two stages: the offline identification stage and the ANC stage. In the identification stage, the primary sound was muted, \(\hat{G}_{h}(z)\) from Equation (4) was obtained, and \(\hat{G}(z)\) was calculated and stored in the library, together with the filter coefficients and \(\tau\), as described in Section 3. In the control stage, different types of primary sound sources were played in turn, setting the \(u(n)\) value shown in Figure 1 to 0, and we obtained the ANC off-spectrum density of the monitor microphone. Then, by changing the program in the DSP, we obtained different noise reduction results. When the primary sound source was located at point (192, 106), the noise reduction effects of different methods were determined, as demonstrated in Figure 7 for different types of primary sound sources. The noise reduction areas are outlined with green dashed lines, and the areas with obvious mirror noise are outlined with red dashed lines. The large \(\theta\) values at this position led to small values of \((d_{2}-d_{1})\). Except for a slight noise reduction effect on the primary sound source below 500 Hz, all three methods had no significant noise reduction effects on the other three types of primary sound sources. Meanwhile, severe mirror noise was generated by [PERSON]'s method, as shown in Figure 7b, and a significant uplift occurred from 1200 Hz to 2200 Hz, as shown in Figure 7d. As \(\theta\) continued to decrease, the value of \((d_{2}-d_{1})\) increased, so the three methods all demonstrated continuously improved noise reduction effects. When the primary sound source was located at point (112, 166), the noise reduction effects of different methods were determined for different types of primary sound sources, as shown in Figure 8. The single-rate method had poor noise reduction effects, while [PERSON]'s method and the method proposed in this study showed significant noise reduction effects, as shown in Figure 8a,b. As shown in Figure 8c, the proposed method gave superior results to those of the other two methods. It is noted that the results of [PERSON]'s method suffered from severe mirror noise, as shown in Figure 8a,b, and a significant uplift occurred from 500 Hz to 2500 Hz, as shown in Figure 8d. With a further decrease in \(\theta\), the noise reduction effect of the single-rate method began to increase regardless of the spectra of the primary sound source. When the primary sound source was located at point (0, 250), the noise reduction effects of different methods for different types of primary sound sources were determined, as shown in Figure 9. In this case, the three methods achieved good noise reduction effects in the low-frequency parts shown in Figure 9a,b, while the result given by [PERSON]'s method still suffered from severe  
Figure 6: Top view of the layout of the experimental system. mirror noise. As shown in Figure 9c, the noise reduction effect of [PERSON]'s method on the primary sound source did not continue to increase with the decrease in \(\theta\), and, as shown in Figure 9d, it still brought a serious noise uplift, as shown in the results.