Previous works introduced control valve stiction detection and quantification methods for closed-loop systems based on the identification of a Hammerstein element between the feedback controller and plant output signals. These techniques each rely upon the fact that the presence of valve stiction introduces nonlinearities in the closed-loop system, yet, little theoretical discussion has been presented which explains the conditions under which these methods will succeed or fail in properly detecting valve stiction. Therefore, the present work uses frequency domain analysis to provide a theoretical investigation of the identification of stiction in otherwise linear closed-loop systems. In this way, the failure of Hammerstein stiction detection techniques to positively identify valve stiction in certain systems in which it known to be present can be explained accordingly.