se characteristics as noise passes through time-invariant systems, e.g. filters. Given a stationary input noise process n(t) and the impulse response h(t) of an LTI system, then the PSD function of the filtered noise process (3.127) This is only approximately true for 1/f noise. In [Kesh82], it is argued that 1/f noise is time-varying in nature but behaves in a time-invariant manner when observed over a sufficiently small window in time. 3.5 LPTV SYSTEM ANALYSIS USING HTMS equals Syy(jw)=H(jw)Snn(jw)H(jw)* (3.128) Here, H(s) = L{h(t)}. By using (3.128), it is possible to show that any colored noise source n(t) can be obtained by passing white noise through an appropriate causal LTI filter. Equation (3.128) is a special case of an important result that will be used later on. Let us be given two noise sources n1(t),n2(t) with a stationary cross-correlation function (3.129) Furthermore, let us be given two time-invariant filters with impulse responses h1 (T) and h2(T). The cross-correlation function of the filtered processes im(1) (3.130) (3.131) the satisfies (3.132) = H1 (s) and H2(s) respectively equal the Laplace transforms of the impulse responses h1(t) and h2(t). 3.5.3.3 Cyclostationary noise As observed from the above, stationarity makes it easy to perform noise computations. Unfortunately, as was discussed above, LPTV system behavior destroys stationarity. From a mathematical point of view, the autocorrelation function no longer solely de- pends upon the time difference T. This is readily seen by considering the elementary mixing operation y(t) = cos(wot)n(t) (3.133) With n(t) stationary and characterized by (3.124), the autocorrelation function of the output process y(t) equals (3.134) This is a function of both T and t. In characterizing noisy input-output behavior of LPTV systems, we therefore need to extend stochastic processes beyond stationary ones. The direction in which to extend the class of relevant noise processes is suggested by a result that was already obtained for stationary colored noise: any