## 2 Theory Review  
In engineering applications, recorded signals often display complex, unpredictable variations due to the stochastic nature of turbulent, high-speed flows. These random signals cannot be described by deterministic functions, necessitating statistical methods for modeling and interpretation. Key techniques include time averaging, which averages a signal over time, and ensemble averaging, which uses multiple samples of the same signal type. Parameters like the probability density function and autocorrelation function characterize these signals, describing amplitude variations and statistical evolution over time. Understanding concepts such as random variables, stationary and ergodic processes and power spectral density (PSD) is critical for effective signal analysis. While a detailed explanation of these concepts is beyond the scope of this paper, readers are encouraged to consult references [43; 44; 45] for further information. Stationary processes, with time-invariant statistical properties, simplify tasks like filtering and spectral analysis. However, real-world signals are often non-stationary, requiring careful assessment of stationarity assumptions to ensure valid results. This paper explores statistical testing of experimental data to identify patterns and trends, analyzing acoustic signals from an ejector nozzle and 16 chevron nozzles. The results demonstrate that trimmed signals are adequate for calculating acoustic metrics, even though real signals often exhibit non-stationary behavior. The study emphasizes verifying stationarity assumptions for meaningful analysis. **Stationarity. Ergodicity**. Statistical analysis is essential when working with real data, as they represent random signals and processes. A key focus is on ergodic signals, where statistical properties can be derived from a single realization over time rather than averaging across multiple realizations. For a process to be ergodic, it must be strictly stationary, though not all stationary processes are ergodic. Ergodicity allows determining moments like mean and autocorrelation through time or ensemble averages, making it a reasonable assumption for many physical processes unless specific exceptions arise. In this study, the non-stationary portions of signals, such as engine start and stop phases, are excluded to ensure reliable results, like calculating SPL for the engine's highest regime. While strict ergodicity cannot be proven, a wide-sense assumption is often reasonable. For a process \(p(t)\), wide-sense stationarity (WSS) requires a constant mean, \(\mu(t)\), a time-independent variance, \(\sigma^{2}(t)\) and an autocorrelation function \(R_{PP}(\tau)\) dependent only on time lag \(\tau\). A WSS process is ergodic if time and ensemble averages are equivalent, simplifying the analysis to specific metrics like mean and autocorrelation. This paper first verifies WSS and ergodicity before extracting meaningful insights from experimental data, demonstrating their significance in signal analysis. **Acoustics metrics. ** In this acoustics data analysis, metrics like time-variant sound pressure level \(L_{p}(t)\), X-weighted equivalent continuous sound pressure level \(L_{\text{Xeq.7}}\), (e.g., often X-weighted A, C, Z), peak sound pressure level \(L_{peak}\) and maximum sound pressure level \(L_{\text{max}}\) are calculated to understand sound behavior over time, assess risks and take precautions to safeguard human health and safety. When the integration period is the entire period of discussion(e.g., the trimmed period for which the process is ergodic), \(T=T_{0}\), then one refers to overall X-weighted sound pressure level, denoted by \(\text{SPL}(X)\) (i.e., X = A, C, Z) or OXSPL. The WSS random process does not have finite energy and, hence, does not possess a Fourier Transform (FT) [39]. Such signals have finite average power and therefore Power Spectrum Density (PSD) analysis is used to investigate if signals that show a correlation in the time domain are also correlated in the frequency domain.