Spectral characterization of feedback linear periodically time-varying systems

Linear periodically time-varying systems are the basis of many practical systems, ranging from electrical networks with periodically time-varying components to filters which incorporate modulators in the signal path. Despite the pervasive use of digital systems, the study of analog time-varying systems can be considered an important branch of applied mathematics and control, with applications to signal processing and communications. Given the well-known modulators filter bank description of a linear periodically time-varying system the spectral transformation between the input and the output would follow readily. This paper shows a simple way to find such a description for a continuous-time linear periodically time-varying system within a feedback loop, motivated by applications such as gated phase-locked loops.