sion of (3.128). Here, the former captures the impact of an LPTV system on a cyclostationary noise process while the latter models the impact of an LTI system on a stationary noise processes. Example (Mixing noise): Consider the elementary downconversion stage in Fig. 3.13. The elements of the HTM corresponding to this stage are determined by (3.74). As an input signal, we apply u(t)=cos(wot)n(t) (3.155) where n(t) is a stationary noise process with its PSD Snn (jw) largely constrained to [-wo/2,000,2]. A possible HPSD matrix for the cyclostationary input process u(t) is given by (3.156) Note the presence of the off-diagonal elements. This denotes that the noise components in different frequency bands are correlated. For the baseband component yo(t) of the noise at the output of the downconversion stage, we find, by means of (3.154) and (3.74), that (3.157) The latter approximation holds for W << W0. When neglecting the cross-correlations between the noise components in the different input frequency bands, i.e. when zeroing the off-diagonal elements in (3.156), we obtain (3.158) For a typical design, (3.158) predicts a noise strength that is a factor two below the correct solution in (3.157). Hence, a stationary noise approximation may be over opti- mistic in predicting output noise levels. 3.6 CONCLUSIONS AND DIRECTIONS FOR FURTHER RESEARCH This concludes our treatment on LPTV system analysis using HTMs. The theoreti- cal results above demonstrate that use of HTMs allows us to extend traditional LTI frequency-domain techniques to the realm of LPTV system analysis. As will be illus- trated by the practical applications in the next chapter, this is of great use in system and circuit design practice. Conclusions and directions for further research By considering the signal content stored on different carrier waves, i.e. in different frequency bands, as independent input signals, a SISO LPTV system can be described as a limiting case of a MIMO LTI system. As a result, the behavior of an LPTV sys- tem can be captured