order, the vector 11As discussed in section 3.3.2, this concerns an interpretation and not a requirement. If, for example, no(t) is chosen to be a white noise process, then it contributes to signal content in all frequency bands. Selecting the nk(t) to be largely constrained to baseband, however, eases interpreting results. 3.5 LPTV SYSTEM ANALYSIS USING HTMS n(t) of noise processes is completely characterized by the correlation matrix E{n(t)n(t-t)*} = [E{nx(t)n/(t-r)*}] (3.138) (3.139) Rnn(t) (3.140) Note that the cross-correlation function Rnkni (T) between any two baseband compo- nents Nk (t) and n (t) is assumed to be stationary. The matrix Rnn(T) is termed a har- monic correlation matrix. Question of course is whether, for an arbitrary cyclostationary noise signal n(t), it is always possible to find a vector n(t) that satisfies both (3.137) and (3.140). A first part of the answer lies in the fact that for a white noise process nw(t), finding such a vector nw(t) is trivial. One could, for instance, simply select nw.o(t)=nw(t) (3.141) (3.142) A choice that is better in line with the interpretation of the nk(t) as equivalent baseband components is given by main= (3.143) In this case, all nw.k(t) are bandlimited within [-wo/2,wo/2] and uncorrelated. The second part of the noise representation problem is solved in section 3.5.3.7. There, it will be shown that LPTV input-output signal processing preserves the existence of a vector representation that satisfies both (3.137) and (3.140). If such a vector exists for the noise process at the input, it is straightforward to derive one that represents the noise process at the output. If we combine both facts above with the definition of cyclostationary noise processes, then it is readily proven that it is always possible to represent a cyclostationary noise process by means of a vector n(t) of stochastic equivalent baseband components- that satisfies both (3.137) and (3.140). For the stochastic characterization of the vector n(t), we rarely use harmonic correla- tion ma