3.22). This requires the magnitude of all eigenvalues of À to be smaller than one. This in turn is equivalent with the Floquet exponents -the eigenvalues of In a@(T,0))=In(A)-having negative real parts. 3.2.3 Frequency-domain approaches Both methods discussed above are time-domain methods. They are well suited for constructing compact models that can be used for simulation (verification). However, they provide little direct insight into the signal transfers induced by an LPTV system. As was outlined in section 3.1.1, these signal transfers are most naturally described in the frequency domain as this closely corresponds with design practice. Different authors in different fields of engineering have made the same observation. This all lead them to introduce a similar matrix-based frequency-domain description for LPTV systems. In [Maas88], analysis of nonlinear microwave mixers drove the idea the harmonic conversion matrix as a means to capture a mixer's small-signal behavior. This harmonic conversion matrix amounts to the harmonic transfer matrix evaluated at the imaginary axis. In order to deal with the oo-dimensional nature of the matrix, the author proposed to truncate it to finite dimensions. However, the treatment in [Maas88] is somewhat incomplete. The structural properties characterizing the conversion matrix are not noticed. Furthermore, topics like noise and stability analysis are not addressed. Almost at the same time and independently, a similar representation was developed in the field of control theory [Were91a, Were91b]. Here, developments were driven by LPTV stability analysis. The representation is called the harmonic transfer function or also the harmonic transfer matrix characterizing an LPTV system. It is derived starting from an integral representation for LPTV operators. Theory is developed in the Laplace domain with frequency-domain analysis being a limiting case as the Laplace variable approaches the imaginary axis. In this way, the Nyquist stability criterion for linear time-invariant system