Let (t) and (t) be two WSS orthogonal random processes.
a. Further define: u(t) = x(t)-2y(t) and v(t)=3x(t)+y(t)
b. Find Ru(tau), Rv(tau), Ruv(tau) and Rvu(tau) in terms of Rx(tau) and Ry(tau).
Let (t) and (t) be two WSS orthogonal random processes. a. Further define: u(t) = x(t)-2y(t)...
,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) If θ is a constant (non-random), is there any value of θ that will make Yl(t) and Y(t) orthogonal? b) if θ is a uniform r.v., statistically independent of x(t) and Y(t), are there any conditions on θ that will make Yı(t) and Y2(t) orthogonal?
,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) If θ is...
Exercise 5. Let X(t) be a WSS process with correlation function 1-Irl, if-1-1S1 0,otherwise. Rx(T) = It is known that when X (t) is input to a system with transfer function H(), the system output Y(t) has a correlation function Ry(T) sin TT = =-TT Find the transfer function H(u
2. (30 points) Let X(t) be a wide-sense stationary (WSS) random signal with power spectral density S(f) = 1011(f/200), and let y(t) be a random process defined by Y(t) = 10 cos(2000nt + 1) where is a uniformly distributed random variable in the interval [ 027]. Assume that X(t) and Y(t) are independent. (a) Derive the mean and autocorrelation function of Y(t). Is Y(t) a WSS process? Why? (b) Define a random signal Z(t) = X(t)Y(t). Determine and sketch the...
Suppose V is a zero-mean Gaussian random variable, and define the random processes X(t) = Vt and Y(t) = V2t for −∞ < t < ∞. a)Find the crosscorrelation function for these two random processes. b)Are these random processes jointly wide-sense stationary?
Suppose V is a zero-mean Gaussian random variable, and define the random processes X(t) = Vt and Y(t) = V2t for −∞ < t < ∞. a)Find the crosscorrelation function for these two random processes. b)Are these random processes jointly wide-sense stationary?
Let X and Y be two independent Bernoulli( 1/2 ) random variables. Define random variables U and V by U = X + Y and V = | (X - Y) | (abs. value)): (a) Find the joint probability mass function of (U, V ). Hints: note that U and V are taking integer values in {0, 1, 2} and {0, 1}, respectively. (b) Determine the covariance Cov(U, V ): (c) Find Var(U), Var(V ) and determine the correlation coeffcient p(U,...
and is X(t) a WSS process?
6.11 Sinusoid with random phase. Consider a random process x(t)-A cos(wot + ?), where wo are nonrandom positive constants and o is a RV uniformly distributed over A and (0, ?), i.e., ? ~11(0, ?). (a) Find the mean function 2(t) of X(t).
The MGFs of two independent random variables X and Y are given by My (t) = e10(et-1) Define U = X + Y and V-X-Y. Compute Corr(U,V).
The MGFs of two independent random variables X and Y are given by My (t) = e10(et-1) Define U = X + Y and V-X-Y. Compute Corr(U,V).
Q1) Let X(t) be a zero-mean WSS process with X(t) is input to an LTI system with Let Y(t) be the output. a) Find the mean of Y(t) b) Find the PSD of the output SY(f) c) Find RY(0) ------------------------------------------------------------------------------------------------------------------------- Q2) The random process X(t) is called a white Gaussian noise process if X(t) is a stationary Gaussian random process with zero mean, and flat power spectral density, Let X(t) be a white Gaussian noise process that is input to...
3.34. Let fXc(t)) and (X,(t)J denote two statistically independent zero n stationary Gaussian random processes with common power spec- tral density given by SX (f) = SX (f) = 112B(f) watt/Hz. Define x(t) = Xe(t) cos(2tht)--Xs(t) sin(2tht) where fo 》 (a) Is X(t) a Gaussian process? (b) Find the mean E(X (t), autocorrelation function Rx (t,t + T), and power spectral density Sx(f) of the process X(t) (c) Find the pdf of X(O) (d) The process X(t) is passed through...