# Signal Enhancement of Helicopter Rotor Aerodynamic Noise Based on Cyclic Wiener Filtering
## 4 Experiment
### Cyclic Frequency Detection  
Antoni proposed a fast computation of the spectral correlation [33]. Therefore, the cyclic spectral correlation density function, \(S_{x}^{\alpha}(f)\), and spectral coherence function, \(\rho_{x}^{\alpha}(f)\), of the target signal were obtained quickly. The detection method of the cyclic frequency was derived from the detection function:  
\[T(\alpha)=\int_{0}^{f_{s}/2}\lvert\rho_{x}^{\alpha}(f)\rvert^{2}\ df \tag{12}\]  
where \(\rho_{x}^{\alpha}(f)\) indicates the cyclic spectral coherence function of the target signal, obtained by Equation (1), and \(f_{s}\) indicates sampling frequency, which is defined as 2500 Hz in the experiment.  
The time period from far to near (18 km to 0 km) was selected for analysis. The cyclic frequencies were first obtained at a close distance and then gradually detected farther away, until the limit distance where the cyclic frequency can be detected was found.  
First, the cyclic frequency detection was performed at 0.89 km. Figure 6 exhibits the cyclic spectrum coherence function graph and the cyclic frequency detection result. The abscissas of these peaks in Figure 6b denote the cyclic frequencies. [PERSON] concluded that rotor aerodynamic noise is characterized by the fundamental cyclic frequency and its multiplier [22; 23]. Thus, the cyclic frequency detection result in Figure 6 was correct.  
Then, the cyclic frequency detection was conducted at 1.548 km. Figure 7 presents the cyclic spectrum coherence function graph and the cyclic frequency detection result of the Robinson R44 helicopter at this distance.  
The cyclic frequency detection was also achieved at 3.568 km, and the results are demonstrated in Figure 8.  
After a lot of tests, the limit distance was revealed to be 4.114 km. Figure 9 illustrates the spectral coherence function and cyclic frequency at this distance. It was suggested that the multiple relationships of the cyclic frequency were not significant.  
Finally, the detection results of cyclic frequency at 17.75 km were obtained, as exhibited in Figure 10. The cyclic frequency of the Robinson R44 helicopter is completely invisible from this graph.  
Figure 6: (a) The cyclic spectrum coherence function graph of the Robinson R44 helicopter at 0.89 km; (b) the cyclic frequency detection results of the Robinson R44 helicopter at 0.89 km.  
Figure 8: (**a**) The cyclic spectrum coherence function graph of the Robinson R44 helicopter at 3.568 km; (**b**) the cyclic frequency detection results of the Robinson R44 helicopter at 3.568 km.  
Figure 7: (**a**) The cyclic spectrum coherence function graph of the Robinson R44 helicopter at 1.548 km; (**b**) the cyclic frequency detection results of the Robinson R44 helicopter at 1.548 km.  
Figure 9: (**a**) The cyclic spectrum coherence function graph of the Robinson R44 helicopter at 4.114 km; (**b**) the cyclic frequency detection results of the Robinson R44 helicopter at 4.114 km.  
As suggested in Figures 6-10, the characteristic of the cyclic frequency gradually changed from clear to fuzzy. This can be explained because with the increase in the distance, there was more and more attenuation as it traveled through the air, resulting in a lower and lower SNR. The comparison of Figures 6-8 demonstrated that the cyclic frequency deviated when the cyclic frequency was detected at different distances. This was induced by the phenomenon of a Doppler frequency shift. The result of cyclic frequency detection was gradually blurred with the increase in the distance. In Figure 10, the cyclic frequency was completely invisible at 17.75 km. This result was consistent with the result of envelope spectrum analysis.