the information that is needed on n(t). Here, E{.} denotes the expected value operator while n(t)* is the adjoint of n(t). In case of Gaussian stochastic processes, the quantities (3.122)-(3.123) even fix the entire PDF [Jayn03, Mid87]. This section develops the formalism necessary to deal with noise injected in LPTV systems. In doing so, it is mainly concerned with a second-order noise characterization (mean and autocorrelation function). It will be seen that traditional stationary noise models -and their power spectral densities (PSDs)- are no longer sufficient to char- acterize the kind of noise produced by LPTV systems. An extended class of noise processes is needed: cyclostationary noise processes. The treatment that follows is to some extent similar to the one in [Royc98]. However, it differs by allowing a non-unique characterization for cyclostationary noise processes. These extra degrees of freedom can, for example, be used to simplify the problem setup. Furthermore, we always assume all noise sources to be zero-mean, or mn(t)=0. Since a non zero-mean noise source can be modeled as the sum of a deterministic signal and a zero-mean noise source, there is no loss in generality. 3.5.3.1 Cyclostationarity: does it matter for design practice? Before introducing a whole set of new concepts for dealing with noise in LPTV sys- items, we pause for a moment and ask the question: is it really needed? What is the problem with traditional noise analysis based on stationary noise models and their power spectral density (PSD) representations? The answer lies in the fact that a sta- tionary noise model assumes the noise content in different, non-overlapping frequency bands to be uncorrelated. Since LPTV systems cause up- or downconversions, they destroy stationarity by intro- ducing cross-correlations between the noise content in different, non-overlapping fre- quency bands. Consider, for example, the leaky upconversion mixer shown in Fig. 3.21. 3.5 LPTV SYSTEM ANALYSIS USING HTMS correlated! correlated! Figure 3.21: Any