5. A stationary random process V (t) having an autocorrelation function Sin(101) Rv.v. (1) - is...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
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?
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
A random process X(t) has an autocorrelation function Rxx (T) = 9 + 2e-1| If X(t) defined in question 11 is the input to a system having an impulse response h(t) = e-stu(t), where is a positive constant Find the mean value of the output process
Problem 5 A Wide-sense stationary random process X(t), with mean value 10 and power spectrum Sxx = 15078(0) +3/[1 + (0/2)?] is applied to a network with impulse response h(t) = 10exp(-4/11) Find (a) H(o) for the network (b) the mean value of the response (C) Syy(Q), the power spectrum of the response
P9.3 A random process X(t) has the following member functions: x1 (t) -2 cos(t), x2(t)2 sin(t), x3(t)- 2 (cos(t) +sin(t)),x4t)cost) - sin(t), xst)sin(t) - cos(t).Each member function occurs with equal probability. (a) Find the mean function, Hx (t). (b) Find the autocorrelation function, Rx(t1,t2) (c) Is this process WSS? Is it stationary in the strict sense?
5. Let X(t) be a random process which consist of the summation of two sinusoidal components as t(t) = A cos(wt) + B sin(wt), where A and B are independent zero mean random variables. (a) (5 points) Find the mean function, pat). (b) (5 points) Find the autocorrelation function Ratta). (e) (5 points) Under what conditions is i(t) wide sense stationary (WSS)?! The questions form the textbook : 1.4, 2.1, 2.4, 2.6 Some trigonometric formulas: cos(A + B) = cos...
Q.6 Determine the autocorrelation function and power spectral density of the random process olt)= m(t) cos(21f t+), where m(t) is wide sense stationary random process, and is uniformly distributed over (0,2%) and independent of m(t).
OLUN An ergodic random process X(T) has the following autocorrelation function: Rx(T) = 36+ 1+67² Determine the mean square value of X(t). a. 57 b. 36 O c 40 d. 24 - A Moving to another question will save this response.