.58) Moreover, HK(s) is a submatrix of HK+1(s). With mild conditions on the behavior of the LPTV operator captured by H(s), use of any such sequence {Hk(s)}, in the limit for K 8, yields the same results. The basic reason for this is that, mostly, the signal energy located beyond a particular finite frequency is of negligible importance. In what follows, we deal with HTMs as if they were finite-dimensional matrices. Unless when relevant, we do not explicitly refer to their co-dimensional structure as this would only complicate expositions. 3.3.6 Matrix-based descriptions for arbitrary LTV behavior 3.3.6 Matrix-based descriptions for arbitrary LTV behavior We conclude this section with some notes on the generalization of the HTM concept to handle other, more general classes of LTV systems. Just as a matrix representation is developed for capturing signal transfers between the harmonic carriers e.imwot it is possible to do SO for systems that transfer signal content between carrier waves 4m(t) other than the harmonic ones. As such, we create a class of LTV systems that can be associated with the carriers Ym(t), just as T-periodic LPTV systems are associated with the harmonic carriers ejiwwot Developing the matrix representation for such systems and unraveling its structural properties proceeds along the same lines as outlined above for LPTV systems. Moreover, although further discussion in this chapter is restricted to linear T-periodic systems, it is worth indicating that most of the analysis that follows is straightforward to generalize. 3.4 LPTV system manipulation using HTMs Having discussed HTMs and their basic properties in depth, we now turn to their use for the manipulation and analysis of LPTV system behavior. Use of HTMs allows us to extend techniques for manipulating LTI systems to handle LPTV ones as well. Section 3.4.1 introduces HTM representations for two types of elementary LPTV sys- items. The basic apparatus for computing the HTMs of composed systems is outlined in sections 3.4.2 and 3.4.3. Togeth