# Question: Let X t be a wide sense stationary Gaussian random

Let X (t) be a wide sense stationary Gaussian random process and form a new process according to Y (t) = X (t) cos (ωt + θ) where ω and θ are constants.

(a) Is Y (t) wide sense stationary?

(b) Is Y (t) a Gaussian random process?

(a) Is Y (t) wide sense stationary?

(b) Is Y (t) a Gaussian random process?

**View Solution:**## Answer to relevant Questions

Let X (t) be a wide sense stationary Gaussian random process and form a new process according to Y (t) = X (t) cos (ωt + θ) where ω and θ are constants and is a random variable uniformly distributed over [0, 2x] and ...A workstation is used until it fails and then it is sent out for repair. The time between failures, or the length of time the workstation functions until it needs repair, is a random variable T. Assume the times between ...Suppose the power line in the previous problem has an impulse response that may be approximated by h (t) = te– atu (t), where a = 10s– 1. (a) What does the shot noise on the power line look like? Sketch a possible ...Consider the random process defined in Example 8.5. The PDF, fX (x; n), and the mean function, µX [n], were found. (a) Find the joint PDF, fX1, X2 (x1, x2; n1, n2). (b) Find the autocorrelation function, RX, X (k, n) = E ...The three letters C, A, and T represent the states of a word- generating system. Let the initial state probability vector be (1/ 3 1/ 3 1/ 3) for the three letters, respectively. The transition matrix is given as What is the ...Post your question