The recently proposed Frequency-Translational Noise-Cancelling receiver demonstrates exceptional out-of-band linearity, a low noise factor, and wideband operation. Fundamental to the receiver's performance is the use of two passive-mixer-based downconversion paths, which delays noise-cancelling until after baseband filtering. As a result, voltage gain at blocker frequencies can be avoided, but the benefits of noise cancelling (i.e., wideband operation and low noise) can be retained. Although a simplified LTI analysis is sufficient to understanding the basic noise properties of the system, such an analysis cannot yield accurate closed-form expressions because it neglects the many signal and noise folding terms introduced by the two passive mixers. In this work, a complete LTV analysis is presented, which accurately captures both the gain and noise performance of the noise-cancelling receiver. Simulation results verify the analysis.