## 4 Results and Discussions
### Ejector Nozzle
#### 4.1.2 Time and Frequency Domain Analysis
Finally, the spectrum sound pressure level \(SPL(f)\) can be determined by  
\[SPL(f)=10\lg\left[\frac{1}{p_{ref}^{2}}\sum_{r=1}^{N_{seg}}\frac{\left|X_{r}(f) \right|^{2}}{f_{s}N_{w}U_{w}}\right] \tag{15}\]  
Figure 8: Acoustics metrics for baseline (**a**) \(L_{p}(t)\), (**b**) \(L_{Adap,T_{o}}\), \(L_{Zap,T_{o}}\), \(L_{Cap,T_{o}}\), (**c**) power spectrum from periodogram, (**d**) spectrum \(\text{SPL}(f)\), (**e**) spectrum SPL (detail) and (**f**) one-sided spectrum. In Figures 8d and 9d, the four algorithms gave very similar results, starting from 50 Hz. Comparing Figure 8d,e and Figure 9d,e, it is noticeable that a frequency appears around 11528 Hz. It is also visible in both the periodogram, Figures 8c and 9c, and the frequency spectrum in Figures 8f and 9f. The explanation for this is that the signal selection was made at the maximum regime of the turbo microjet, operating at a rotational speed of 115,179 RPM (\(n=1919\) rev/s) for the baseline and 115,486 RPM (\(n=1924\) rev/s) for ejector. The micromotor is equipped with a centrifugal compressor with \(B=6\) blades, and the theoretical frequency is \(f_{theoretical}=B\cdot n=11,549\) Hz. The theoretical frequency calculated based on the RPM and the compressor's blade count aligns closely with the measured frequency, confirming that this feature is a result of the compressor's operation. To conclude, the detected frequency is a characteristic signature of the centrifugal compressor at the specified operating conditions. Moreover, the ejector increases slightly the magnitude of the beat, indicating that the beat is not a significant contributor. Figure 9: Acoustics metrics for ejector (**a**) \(L_{p}(t)\), (**b**) \(L_{A\text{eq},\text{T}}\), \(L_{Z\text{eq},\text{T}e}\), \(L_{C\text{eq},\text{T}o}\), (**c**) power spectrum from periodogram, (**d**) spectrum \(\text{SPL}(f)\), (**e**) spectrum SPL (detail) and (**f**) one-sided spectrum. the spectrum SPL from 83 dB to 86 dB, which is not a bad thing because frequency is higher than 8 kHz. On the other hand, in the case of peaks in the lower frequency range, a decrease in SPL is observed. For example, at a frequency of 270 Hz, there is a peak of 102.4 dB in the baseline configuration, while in the configuration with the ejector, at approximately the same frequency, it is 101.8 dB. Similarly, at 1289 Hz, which is the fundamental harmonics of the compressor, the baseline shows an SPL = 98.3 dB (n.b. the magnitude of the spectrum is 0.547 Pa), whereas the ejector configuration registers SPL = 94.5 dB (n.b. the magnitude of this peak is decreased up to 0.226 Pa). The final analysis of this topic focuses on the observation that, at first glance, Figures 8d and 9d reveal very similar results across all four algorithms. However, Table 5 shows very small differences in the SPL values obtained using the four methods for both configurations, (B) and (E). Although the values are extremely close, the spectrogram and Short-Time Fourier Transform (STFT) methods tend to give slightly higher values, especially for configuration \"E\", while the in-house code, the power spectrogram and the SPL(Z) calculated using the pressure fluctuations, provide almost identical results.