cut interpretation to the elements of Snn(jw): the diagonal element Snknk (jw) captures the autocorrelation of the noise content in the k-th frequency band; the off-diagonal element Snkni (jw) (for k #1) captures the cross-correlation between the signal content in two different (non-overlapping) frequency bands. 3.5.3.6 Properties of a HPSD matrix Although the choice of the stochastic baseband components nk(t) is to some extent arbitrary, different HPSD matrices Snn (jw) that characterize the same cyclostationary noise process n(t) do have a number of properties in common. Semi-positive definiteness A first property of a HPSD matrix Snn (jw) is its semi-positive definiteness for any W E R. This follows directly from the properties of PSDs of stationary noise sources. Given a complex-valued vector X = 1st it is easily verified that the process nx(t)=x*n(t) (3.145) is stationary with its PSD satisfying (3.146) The latter inequality follows from the properties of stationary noise processes. Since X is arbitrary, (3.146) implies that the HPSD matrix Snn(jw) is a semi-positive definite matrix for any WER. Structural constraints As was already mentioned, it is possible to characterize the same overall cyclostation- ary noise process n(t) by means of different HPSD matrices Snn (jw). This corresponds to different choices for the baseband components Nk k(t). However, all HPSD matrices associated with a same noise process n(t) will have a number of quantities in common. These quantities are revealed by expressing the autocorrelation function Rnn (t,t) of the overall cyclostationary process n(t) in terms of the elements of a possible HPSD matrix Snn(jw). Using (3.137) and some algebra, we obtain Rnnt,t)=E{n(t)n(t-t)} (3.147) k=-00 3.5 LPTV SYSTEM ANALYSIS USING HTMS with coefficients Rnn,k(t) that equal (3.148) Here, the Rnk+1n (T) are the elements of the harmonic correlation matrix Rnn(T) defined in (3.139). The PSDs associated with the Rnn,k(t) are then given by (3.149) Observing (3.147), it is seen that Rnn(t,T) is peri