Cross-correlation functions between synthetic spectra with added Gaussian noise and containing ¹³CO generated using Exo-REM and their associated model spectrum. Gaussian noise at different levels (S/N = 10, 20, and 30) was applied to each synthetic spectrum. Top: CCFs without atmospheric noise. Bottom: CCFs with atmospheric noise. The signal is clearly detected for the spectrum with S/N = 30 without atmospheric noise, with a detection significance of S/N_CCF = 3.85.