,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) I...
Consider two random processes X(t) and Y(t) defined as X(t)=Acos(wot+z), Y(t)=Bsin(wo+z) where A and B and wo are constants and z is a random variable that is uniformly distributed between 0 and 2pi. find the cross-correlation function of X(t) and Y(t). If both X(t) and Y(t) were wide sense stationary , could they also be jointly wide sense stationary?
Problem # 11: Let Y(t) = (a + a X(t) cos(20 ft+), where a; are constants, 0 is uniform on (0,27], X(t) is a random process independent of 8 at all time instants and is WSS. Determine the mean and the covariance function of the process Y(t). Is Y(t) WSS?
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).
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 X and Y be defined by: X = cos Y = sino Where is a uniformly distributed r.v. between 0 and 21. a) Show that X and Y are uncorrelated. b) Show that X and Y are not independent.
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...
The sample function X(t) of a stationary random process Y(t) is given by X(t) = Y(t)sin(wt+Θ) where w is a constant, Y(t) and Θ are statistically independent, and Θ is uniformly distributed between 0 and 2π. Find the autocorrelation function of X(t) in terms of RYY(τ).
Let X(t) be a wide-sense stationary random process with the autocorrelation function : Rxx(τ)=e-a|τ| where a> 0 is a constant. Assume that X(t) amplitude modulates a carrier cos(2πf0t+θ), Y(t) = X(t) cos(2πf0t+θ) where θ is random variable on (-π,π) and is statistically independent of X(t). a. Determine the autocorrelation function Ryy(τ) of Y(t), and also give a sketch of it. b. Is y(t) wide-sense stationary as well?
Three random variables A, B, and C and 1. The random processes X(t) and Y (t) answer the questions below. (24 points) independent identically distributed (id) uniformly between are defined by the given equations. Use this information to are X(t) = At + B Y(t) = At + C (a) Find the autocorrelation function between X(t) and Y(t) (b) Find the autocovariance function between X (t) and Y(t). (c) Are X(t) and Y(t) correlated random processes? Three random variables A,...
The random process X(t) is defined by X(t) = X cos 27 fot + Y sin 2 fot, where X and Y are two zero-mean Gaussian random variables, each with the variance 02. (a) Find ux(t) (b) Find RX(T). Is X(t) stationary? (c) Repeat (a) and (b) for 0 + 0