odic in t since it can be expanded in a Fourier series. Furthermore, (3.149) shows us how to interpret the PSD Snn,k(jw) associated with the k-th Fourier coefficient Rnn.k(t): the amount of energy in Snn,k(jw) in the band around two is a measure for the strength of the cross-correlation between the noise components in the frequency bands around respectively two and (k+1) W0. Since the quantities Snn,k(jw) are unique, the relation (3.149) represents a number of structural constraints that must be satisfied by all different HPSD characterizations of a same cyclostationary noise process n(t). Whatever characterization is used, the sum on the right-hand side of (3.149) does not vary from one characterization to another. As a final note, we mention that (3.149) allows us to construct a uniquely determined HPSD matrix. If the baseband components Nk (t) are constrained to to [-wo/2,wo/2], then the same holds for all corresponding HPSD matrix elements Snkni (jw). Using (3.149), we then find that (3.150) for w E [-wo/2,wo/2] while equal to zero elsewhere. Hence, imposing bandwidth restrictions on the nk(t) hence results in a uniquely determined HPSD matrix. 3.5.3.7 Noise computations using HTMs and HPSD matrices Next, we address the characterization for the output y(t) of an LPTV system to which a cyclostationary input signal n(t) is applied. Hereby, we keep in mind that LPTV oper- ators preserve cyclostationarity. Hence, we look for a HPSD matrix that characterizes (3.151) Here, h(t,T) is an LPTV system kernel. With H(s) the HTM associated with h(t,T), it follows from (3.137) and the HTM-based input-output relation (3.43) that (3.152) Here, (3.153) 3.5.3 Noise analysis with hi,k(t) = -1{HI,k(s)} Using (3.132) it is then readily obtained that the matrix y(jw)=H(jw)Snn(jw)H(jw)* (3.154) represents a valid HPSD matrix that characterizes the correlations between the base- band components y1(t). Note that all correlations between the different components yl(t) remain stationary. The relation (3.154) is a straightforward exten