Frequency-Domain Analysis of Linear Time-Periodic Systems

In this paper we study how a system with a time-periodic impulse response may be expanded into a sum of modulated time-invariant systems. This allows us to define a linear frequency-response operator for periodic systems, called the harmonic transfer function (HTF). Similar frequency-response operators have been derived before for sampled-data systems and periodic finite-dimensional state-space systems. The HTF is an infinite-dimensional operator that captures the frequency coupling of a time-periodic system. The paper includes analysis of convergence of truncated HTFs. For this reason the concepts of input/output roll-off are developed and related to time-varying Markov parameters