Consider a Gaussian random process X(t) with a zero mean, i.e., E{X(t)}=0, and = the following autocorrelation function:

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Consider A Gaussian Random Process X T With A Zero Mean I E E X T 0 And The Following Autocorrelation Function 1 (283.63 KiB) Viewed 40 times

Consider a Gaussian random process X(t) with a zero mean, i.e., E{X(t)}=0, and = the following autocorrelation function: Rxx (T) = E{X(t +T)X(t)}; = N. -8(T) 2 Let Y(t) be the output of the linear-time invariant system with the impulse response of h(t) as follows: X(t) h(t) →Y(t) where h(t)=1000sinc(1000t). (a) Find the autocovariance function of Y(t) (b) Find the expected value of Y(t). (c) Find the average power of Y(t). (d) Find the joint probability density function of Y(t) and Y(t2), i.e., fy(6)Y()(yı, y2), assuming that | t; – tą l= 0.001. Note: A joint probability density function of the Gaussian random vector X = (X1, X2,---,X,) is given as 1 fg(x) = fx.xx.x, (X7 , X2 ... X,) = exp{-} (x-m (x-mx)"C'(x-mx)} (21)|Cy\