principle of superposition still holds. Systems that exhibit this kind of behavior are termed linear periodically time-varying (LPTV). Handling LPTV system behavior requires us to extend traditional techniques used for linear time-invariant (LTI) system analysis. A single scalar transfer function is unable to capture signal transfers from one frequency band to another. This chapter elaborates a framework for frequency-domain LPTV system analysis based on harmonic transfer matrices. Applications of the framework are presented in the next chapter. A HTM-based representation considers the signal content in each frequency band as separate and independent inputs. In this way, a single-input single-output (SISO) LPTV system can be modeled as a multi-input multi-output (MIMO) LTI system. Hereby, the contents of the different frequency bands are treated as different inputs. Hence, LPTV behavior can be captured using a matrix of transfer functions, called a harmonic transfer matrix (HTM). Each HTM element models the transfer of signal content from a particular input frequency band to a particular output frequency band. The basic concepts underlying the HTM framework are outlined in section 3.1. The mathematical details are discussed in section 3.3. HTMs allow us to adapt many techniques for frequency-domain analysis of LTI sys- tems to handle LPTV systems as well. With regard to this matter, section 3.4 discusses the construction of HTMs for elementary LPTV systems. It also outlines how to com- pute HTMs of composed systems. Finally, section 3.5 treats stability and noise analysis of LPTV systems. A major problem in performing HTM-based computations lies in a HTM's infinite dimensional matrix structure. Prior art (see section 3.2) has dealt with this problem by truncating the HTM to some large but finite size. However, when this size grows large, matrix computations become very tedious. This especially holds for HTM inver- sions -needed for feedback computations- and eigenvalue computations -needed for stability analysis.