## 4 Experimental Results
### Noise Reduction Performance  
Narrowband noise is noise whose energy is mainly concentrated at a specific frequency or at several specific frequencies. This noise is common in periodic noise sources, such as  
Figure 5: The white Gaussian input: (**a**) the relative modeling error \(\Delta w(n)(dB)\); (**b**) the time-varying step-size upper bound parameter \(\mu_{\text{max}}(n)\). The first-order AR process input: (**c**) the relative modeling error \(\Delta w(n)(dB)\); (**d**) the time-varying step-size upper bound parameter \(\mu_{\text{max}}(n)\). engine noise. We selected single-frequency, multi-harmonic-frequency, and fixed-frequency band noise for the experiments. The mean value of the white noise signal used in the experiment was 0 and the variance was 1000. The order of the secondary path filter is 128. The value of K is 6. As shown in Figure 6, with an increase in ANC filter order, the noise reduction effect of the system was better. The increase in filter order will obviously challenge the computing resources of the system. When the bandwidth of the reference noise signal is small, the computational pressure on the control system can be reduced by reducing the order of the ANC filter. Due to the influence of the electric heating noise of the ANC system and irrelevant background noise in the environment, residual noise remained at the noise control point when the system was stable. The higher the orders of the ANC filter, the faster the convergence speed of the system. From Figure 6d, we can see that, if the order continues to increase, the improvement in the convergence speed of the system is not obvious. When the order of the ANC filter was 20, the ANC system also achieved a good noise reduction effect under the guarantee of convergence speed. Therefore, a relatively small ANC filter order can obtain a significant noise reduction effect when dealing with noise with a relatively single-frequency component. Figure 6: Comparison of noise reduction performance when the reference signal is 400 Hz. **(a)** The order of the ANC filter is 10; **(b)** the order of the ANC filter is 20; **(c)** the order of the ANC filter is 30; **(d)** power changes in error microphone signal (e) at different ANC filter orders. As shown in Figure 7, noise control was performed on noise with multi-harmonic-frequency components. The multi-harmonic noise components were 200 Hz, 400 Hz, 600 Hz, and 800 Hz. Different orders were used to deal with the multi-harmonic noise. As the noise signal became complex, higher requirements were proposed for the order of the ANC filter. In the noise reduction in single-frequency noise, when the order of the ANC filter was 10, a noise reduction of more than 10 dB was achieved. However, for noise with multi-harmonic frequency, when the order of the ANC filter increased to 30, the residual error signal at the error microphone was greatly reduced, the overall noise reduction in the system reached 30 dB, and the convergence speed was obviously accelerated. Increasing the order of the ANC filter cannot further improve the convergence speed and the steady-state error of the system. Therefore, considering the hardware resources and selecting the appropriate order, the system can achieve a significant noise reduction effect. The noise reduction effect at 200 Hz was better than that at 800 Hz. This also showed that the noise reduction effect of the system decreased with the increase in noise frequency. In practical applications, noise energy is concentrated in a specific frequency band. Therefore, it is necessary to verify the noise reduction effect of the system on narrowband  
Figure 7: Comparison of noise reduction performance when the reference signal is multi-harmonic. (**a**) ANC filter order is 20; (**b**) ANC filter order is 30; (**c**) ANC filter order is 40; (**d**) the power change in error microphone signal e(n) when ANC filter order is different. noise. The noise band selected was 200-600 Hz, and the order of the ANC filter was 10, 25, and 40.