 by a matrix of transfer functions, called a HTM. Techniques for multi-variable LTI system analysis and design can therefore be applied to analyze the behavior of LPTV systems. These techniques are made efficient by exploiting both the structure inherent to HTMs and the properties of HTMs as they occur in practical ap- plications. This results in a consistent framework for handling LPTV system analysis. Furthermore, the theory has been presented in a manner that is straightforward gen- eralize towards other classes of LTV systems. These classes are then associated with sets of carrier waves other than the harmonic functions {Ym(t) = e.jmwot used in this chapter. Suggested directions for further research involve, for instance, linear quasi- periodic time-varying system analysis and the use of principal component analysis for the autodetection of relevant sets of carrier waves. The former is useful to analyze the behavior of heterodyne transceiver stages, while the latter can, for example, be applied to capture the noise behavior of nonlinear systems. Chapter 4 Applications of LPTV system analysis using harmonic transfer matrices Whoever in the pursuit of science, seeks after immediate practical utility may rest assured that he seeks in vain. -Hermann von Helmholtz armonic transfer matrices (HTM) constitute a natural framework for frequency- domain analysis of linear periodically time-varying (LPTV) system behavior. They directly describe how an LPTV system transfers signal content from one fre- quency band to another. Furthermore, HTMs not only satisfy from a theoretical point of view, they also have numerous practical applications. This chapter illustrates the prac- tical use of HTMs for analyzing phase-locked loop (PLL) and mixer behavior. Hereby, special focus is given to symbolic results and techniques to obtain them. These sym- bolic results are most useful for guiding design decisions. It demonstrates the power of HTM-based analysis as a practical means to capture a circuit's time-varying small- signal behav