## 3 Materials and Methods
### Processing of the Acoustic Signals  
The acoustic signals measured in experiments and predicted computationally are compared. They are obtained using different sampling frequencies and sample lengths. There are many techniques used to prepare such data for comparison, and the methods used in this paper are described here. The processing of the computational data is discussed first. In PSU-WOPWOP, surface pressures are integrated to obtain the field pressure at the appropriate retarded time. Thus, the field pressure experiences a start-up effect in which there are no disturbances that have propagated to the point at the initial time, and as time progresses, disturbances from different surface locations begin to arrive. This start up manifests as a large pressure spike near the beginning of the audible time history. When the field pressure can be assumed to be periodic, the solver can assume that the end of the period can be wrapped into the beginning of the period filling in the disturbance information at the early times. Often, this leads to a regular field pressure signal. A drawback of the periodic assumption, though, is that only one period of computational data is used, which limits the frequency resolution of the associated spectrum. To ensure better frequency resolution, five rotor revolutions were used for the acoustic integration in this paper. A periodic assumption was still made to try to avoid the effects of the initial acoustic spike. However, a spike still appeared in the first revolution as seen in Figure 4, which depicts the acoustic pressure signal at an above-plane observer of a dual rotor simulation, using Helios/PSU-WOPWOP. This most likely indicates that the simulation had not reached a perfectly periodic state when the acoustic integrals were started. Researchers often employ a Hanning window when computing the spectrum of the acoustic signal [7; 8; 25]. It serves to dampen transient issues that can arise at the beginning and end of the pressure signal. A Hanning window is best used on longer signals than we have at our disposal in this work. Figure 4 shows the Hanning window applied to the five cycles of data we have at a given field point. The alteration to the signal at the beginning and end of the sampling can be seen in the left plot. The FFT of the original signal and the signal with the Hanning window applied is presented in the right plot. The Hanning window alters the tones and the broadband. Another approach to avoid the spike is to simply ignore the first revolution of the field pressure data. When an FFT is taken over the last four revolutions (and then adjusted for the differing frequency resolution via the power spectral density (PSD)), the nature of the signal is not as affected as when the Hanning window is applied as shown in Figure 4b. The overall sound pressure level was computed over the frequency band of 50 Hz to 10 kHz and included in the legend for each signal. The Hanning window dampens the energy of both the tones and the broadband. This results in a drop in the overall sound pressure level, compared to the other cases, and is not a good representation of the total noise. Therefore, the processing in this paper computes the acoustic pressure at the field point for five revolutions but will use only the last four revolutions to obtain the spectrum. Next, the experimental measurements were prepared for comparison with simulations. The large sampling time of the experiments, 5 s, corresponds to 500 rotor revolutions. This leads to a frequency resolution much finer than that of the 4 or 5 rotor revolutions available from Helios/PSU-WOPWOP. The broadband amplitude spectra cannot be directly compared due to the differing frequency resolution. The PSD corrects for this difference by normalizing the spectral energy by the resolution, but should only be applied to the broadband, as the tones are unaffected by these issues, due to their periodicity. Therefore, ensemble averaging is typically employed to equalize the frequency resolution of the experiments with the simulations.