ed LPTV system analysis The HTM-based analysis of LPTV system behavior considers the signal content stored on different carrier waves, i.e. in different frequency bands, as independent input sig- nals. In this way, a SISO LPTV system can be described as a limiting case of a MIMO LTI system. As a result, the behavior of an LPTV system can be captured by a matrix of transfer functions. Each transfer function models the transfer of signal content from a particular input frequency band to a particular output frequency band. The prop- erties and the behavior of LPTV systems can then be analyzed using techniques for multi-variable LTI systems. This results in a powerful framework for handling LPTV system behavior, including the analysis of signal transfers, stability analysis and noise analysis. A major bottleneck in making HTM-based techniques practical is the co-dimensional nature of a HTM. In principle, there are an infinite number of frequency bands that must be taken into account. When not handled carefully, this rapidly leads to computations that involve huge matrices [Molloo, Royc98, Royc99]. Although these matrices can be dealt with by means of sparse-matrix techniques, it is, in many cases, by far a sub- optimal solution. This work has presented a number of methods that overcome these difficulties. These methods avoid tedious computations on huge matrices by exploiting both the structure inherent to HTMs and the properties of HTMs as they occur in design practice. In this way, they render HTM-based analysis of LPTV systems practical, both for obtaining numerical results and symbolic expressions. The usefulness of the HTM framework was demonstrated by means of two applica- tions: the analysis of PLL behavior and the SymbolicHTM algorithm. HTMs support an exact description of the time-varying aspects of a PLL's small-signal behavior. This time-varying behavior is inherent to all practical PLL implementations. Existing LTI techniques for PLL modeling were shown to coincide with specific approximations to the exac