Ramirez Delgado, Victor2023-10-092023-10-092023https://udspace.udel.edu/handle/19716/33516The Rayleigh criterion determines the resolution limit of a periodogram, which is the minimum frequency separation required to barely resolve two sinusoids. Neglecting to consider the Rayleigh criterion may result in a false interpretation of a long-period signal or a spurious claim that two closely spaced periodogram peaks represent two distinct physical processes. This thesis demonstrates how the Rayleigh criterion can help astronomers avoid false positives caused by artifacts of uneven time intervals between observations. We use the Rayleigh criterion to show that the frequency separation between planet 55 Cncd and the stellar activity cycle is too small to distinguish the two phenomena based on published radial velocity data alone. We also demonstrate that the radial velocity signal of contested planet HD99492~c cannot be separated from zero frequency according to the Rayleigh criterion. Finally, we demonstrate that a cubic polynomial is a better fit to the long-term RV variability of Barnard's star than a sinusoid with a frequency that is statistically indistinguishable from zero. This work concludes that astronomers searching for periodic signals should consider the Rayleigh resolution criterion as part of their discovery validation.Exoplanet detectionsExoplanetsRadial velocitiesRayleigh criterionThesis1416508824https://doi.org/10.58088/6g6y-sw042023-09-20en