## 4 Results and Discussion
Using FFT to analyze the evolution of indoor Rn concentration allows for examining the seasonal periodicity in the Rn concentration in the frequency domain, which can be influenced by factors such as alterations in ventilation procedures of the area, modifications in occupancy patterns (resulting in changes in ventilation patterns and thermal comfort, among other things), or broader changes in a seasonal nature related to meteorological parameters (temperature, atmospheric pressure, and relative humidity), as well as geogenic factors such as the water table level and soil porosity. In this way, by applying FFT to the time series of Rn concentration, it is possible to identify the frequency components that contribute to its seasonal periodicity. For example, there may be a daily frequency component due to changes in the ventilation of the environment, or a seasonal frequency component due to changes in temperature. To apply the FFT, the stationarity in the time series was verified by checking if the mean and variance of the time series are constant over time. In the case presented, the analysis of stationarity in the time series was achieved using visual inspection, as projecting the data showed consistency in the evolution of the results, indicating that the mean and variance appear to be constant (or approximately constant) over time. The analysis of the mean and variance of the series in consecutive time intervals (in this case, with the analysis of the periods indicated in Figure 3) also confirmed that they are constant over time. Finally, the augmented Dickey-Fuller (ADF) test was used, which tests the null hypothesis that the series is non-stationary. As \(p<0.05\) in this case, the null hypothesis was rejected, and the series is considered stationary. For this determination, an R routine with the RStudio software (Version 2022.12.0 + 353) was used. As there are no missing data in the time series, there is no need to apply an imputation or data cleaning technique. In this case, Microsoft Excel's Data Analysis package (Version 16.68) was used, which includes Fourier Analysis. The Fast Fourier Transform (FFT) in Excel does not impose a specific order. However, to achieve the most accurate and efficient results, it is advisable to ensure that the number of data points is a power of 2. The reason for this is that the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Time Interval** & **Positive Increments** & **Minimum Registered Value** & **Maximum Registered Value** & **Average** \\  & **(n)** & **(Bq\(\cdot\)m\({}^{-3}\)\(\cdot\)h\({}^{-1}\))** & **(Bq\(\cdot\)m\({}^{-3}\)\(\cdot\)h\({}^{-1}\))** & **(Bq\(\cdot\)m\({}^{-3}\)\(\cdot\)h\({}^{-1}\))** \\ \hline
1 & 78 & 0.1 & 26.1 & 5.41 \\
2 & 73 & 0.1 & 25.5 & 3.95 \\
3 FFT algorithm continuously divides the data into smaller pairs until each pair contains only one data point. If the number of data points is not a power of 2, the FFT will not be able to evenly divide the data. To overcome this issue, it may be necessary to pad the data with additional zeros to achieve the appropriate number of data points. However, since there is a sufficient number of data points, we opted to compute the FFT with an order of 512 samples. Figure 4 schematizes the overlap in the data obtained from the indoor Rn concentration monitoring campaign (orange line) and the results obtained from the FFT (black line).