# Signal Enhancement of Helicopter Rotor Aerodynamic Noise Based on Cyclic Wiener Filtering
## 4 Experiment
### Filtering  
The cyclic frequencies of rotor aerodynamic noise at different distances were obtained, and then the frequency shift was carried out according to the cyclic frequency detection method in Section 4.1. The detection results of several groups of cyclic frequencies are given in Table 2, which are used in the following cyclic Wiener filter. Since the aerodynamic noise of the main rotor of the helicopter is mainly in low frequency, it should be band-pass filtered first to filter out some irrelevant background noise, followed by cyclic Wiener filtering. The cyclic frequency, \(\eta\), was inputted for frequency shifting, and the signal after the band-pass filter was taken as the expected response, so as to filter out the background noise adaptively. The filtering effects of the three distance points are exhibited in Figures 7, 9 and 10, respectively. Figure 11 displays the envelope spectrum of the Robinson R44 helicopter before and after filtering at 1.548 km. Compared with Figures 11a and 11b, there was less attenuation when propagating in the air owing to the short distance, contributing to a high SNR. Therefore, the characteristics before filtering were significant. Moreover, the characteristics of target information can be observed more clearly through the envelope spectrum after cyclic Wiener filtering. \begin{table}
\begin{tabular}{c c} \hline
**Distance/km** & **Cyclic Frequency/Hz** \\ \hline
0.89 & \(\eta=\) [14.5 29.0 43.5 57.99 72.49] \\
1.548 & \(\eta=\) [15.0 29.5 44.5 58.99 73.99] \\
3.568 & \(\eta=\) [15.5 51.0 46.5 61.99 77.49] \\
4.114 & \(\eta=\) [15.5 31.0 46.5 61.99 77.49] \\ \hline \end{tabular}
\end{table} 
Table 2: Detection results of cyclic frequencies at different distances. Figure 10: (**a**) The cyclic spectrum coherence function graph of the Robinson R44 helicopter at 17.75 km; (**b**) the cyclic frequency detection results of the Robinson R44 helicopter at 17.75 km. At the distance of 4.114 km, the cyclic frequency obtained from Table 2 is \(\eta=\) [15.5 31 46.5 61.99 77.49], and it is applied to the frequency shift of cyclic Wiener filtering. The filtering result is shown in Figure 12.  
The filtering effect of the Robinson R44 helicopter at 4.114 km is presented in Figure 12. As revealed by comparing Figures 12a and 12b, there was more attenuation when propagating in the air because the position here is far away, leading to a low SNR. Therefore, the characteristics before filtering are not significant, and the characteristics of helicopter rotor aerodynamic noise can be observed through the envelope spectrum after cyclic Wiener filtering. After cyclic Wiener filtering is performed point by point, it was discovered that the limit distance of the rotor aerodynamic noise characteristic observed through the envelope spectrum after filtering was 17.75 km, in line with Figure 10. At 17.75 km, the cyclic frequency cannot be detected at all. However, in comparison with Figures 6-8, it can be seen that the farther the distance is, the higher the cyclic frequency is, relatively. Therefore, when inputting the cyclic frequency to conduct a frequency shift over a long distance, the cyclic frequency needs to be increased properly. After multiple attempts, the cyclic frequency, \(\eta=\) [15.75 31.13 44.98 62.19 77.82], was finally selected to conduct a frequency shift. The envelope spectrum before filtering with a distance of 17.75 km is provided  
Figure 11: (**a**) Envelope spectrum of the Robinson R44 helicopter before filtering at 1.548 km; (**b**) Envelope spectrum of the Robinson R44 helicopter after filtering at 1.548 km. Figure 12: (**a**) Envelope spectrum of the Robinson R44 helicopter before filtering at 4.114 km; (**b**) Envelope spectrum of the Robinson R44 helicopter after filtering at 4.114 km. in Figure 13a. The characteristics of the target information were not observed through this envelope spectrum. The filtered envelope spectrum is exhibited in Figure 13b. The characteristics of the target information were observed through several spectral lines in the figure.