Homework Answers
Option C is correct.
We know that Rxx(T)=Rxx(0).
Substitute 0 in place of T in the given autocorrelation function. We get,
Mean Square value of x(t)=40
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OLUN An ergodic random process X(T) has the following autocorrelation function: Rx(T) = 36+ 1+67² Determine...
A random process X(t) has an autocorrelation function Rxx (T) = 9 + 2e-1| If X(t)...
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
Consider a random process X(t) defined by X(t) - Ycoset, 0st where o is a constant 1. and Y is a uniform random variabl...
Consider a random process X(t) defined by X(t) - Ycoset, 0st where o is a constant 1. and Y is a uniform random variable over (0,1) (a) Classify X(t) (b) Sketch a few (at least three) typical sample function of X(t) (c) Determine the pdfs of X(t) at t 0, /4o, /2, o. (d) EX() (e) Find the autocorrelation function Rx(t,s) of X(t) (f) Find the autocovariance function Rx(t,s) of X(t)
Consider a random process X(t) defined by X(t) -...
Let X(t) be a wide-sense stationary random process with the autocorrelation function :
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?
Question 6(20 points) The autocorrelation function of a random process is given by R(r)-81 +8e cos2r+4cos6r...
Question 6(20 points) The autocorrelation function of a random process is given by R(r)-81 +8e cos2r+4cos6r Find (a) The mean value, &, the mean-square valuc, E[X2), and the variance of the random variable X(t). (b) What discrete frequency components (in H2Z) are present
P9.3 A random process X(t) has the following member functions: x1 (t) -2 cos(t), x2(t)2 sin(t),...
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?
2. Consider the random process x(t) defined by x(t) a cos(wt + 6).where w and a...
2. Consider the random process x(t) defined by x(t) a cos(wt + 6).where w and a are constants, and 0 is a random variable uniformly distributed in the range (-T, ) Sketch the ensemble (sample functions) representing x(t). (2.5 points). a. b. Find the mean and variance of the random variable 0. (2.5 points). Find the mean of x(t), m (t) E(x(t)). (2.5 points). c. d. Find the autocorrelation of x(t), R (t,, t) = E(x, (t)x2 (t)). (5 points)....
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...
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...
324. Consider the random process X(t) = A + Bt2 for - <t < oo, where...
324. Consider the random process X(t) = A + Bt2 for - <t < oo, where A and B are two statistically independent Gaussian random variables, each with zero mean and variance o?. a) Plot two sample functions of X(t). b) Find E{X(0)} c) Find the autocorrelation function Rx(t,t +T). d) Find the pdf of the random variable Y = X(1). e) Is X(t) a Gaussian process? Prove your result.
2. Consider the random process x(t) defined by x(t) a cos(wt 6), where w and 0 are constants, and a is a random variable uniformly distributed in the range (-A, A). a. Sketch the ensemble (sample...
2. Consider the random process x(t) defined by x(t) a cos(wt 6), where w and 0 are constants, and a is a random variable uniformly distributed in the range (-A, A). a. Sketch the ensemble (sample functions) representing x(t). (2.5 points). b. Find the mean and variance of the random variable a. (5 points). c. Find the mean of x(t), m(t) E((t)). (5 points). d. Find the autocorrelation of x(t), Ra (t1, t2) E(x (t)x2 )). (5 points). Is the...
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
Consider a random process X(t) defined by X(t) - Ycoset, 0st where o is a constant 1. and Y is a uniform random variable over (0,1) (a) Classify X(t) (b) Sketch a few (at least three) typical sample function of X(t) (c) Determine the pdfs of X(t) at t 0, /4o, /2, o. (d) EX() (e) Find the autocorrelation function Rx(t,s) of X(t) (f) Find the autocovariance function Rx(t,s) of X(t)
Consider a random process X(t) defined by X(t) -...
Question 6(20 points) The autocorrelation function of a random process is given by R(r)-81 +8e cos2r+4cos6r Find (a) The mean value, &, the mean-square valuc, E[X2), and the variance of the random variable X(t). (b) What discrete frequency components (in H2Z) are present
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?
2. Consider the random process x(t) defined by x(t) a cos(wt + 6).where w and a are constants, and 0 is a random variable uniformly distributed in the range (-T, ) Sketch the ensemble (sample functions) representing x(t). (2.5 points). a. b. Find the mean and variance of the random variable 0. (2.5 points). Find the mean of x(t), m (t) E(x(t)). (2.5 points). c. d. Find the autocorrelation of x(t), R (t,, t) = E(x, (t)x2 (t)). (5 points)....
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...
324. Consider the random process X(t) = A + Bt2 for - <t < oo, where A and B are two statistically independent Gaussian random variables, each with zero mean and variance o?. a) Plot two sample functions of X(t). b) Find E{X(0)} c) Find the autocorrelation function Rx(t,t +T). d) Find the pdf of the random variable Y = X(1). e) Is X(t) a Gaussian process? Prove your result.
2. Consider the random process x(t) defined by x(t) a cos(wt 6), where w and 0 are constants, and a is a random variable uniformly distributed in the range (-A, A). a. Sketch the ensemble (sample functions) representing x(t). (2.5 points). b. Find the mean and variance of the random variable a. (5 points). c. Find the mean of x(t), m(t) E((t)). (5 points). d. Find the autocorrelation of x(t), Ra (t1, t2) E(x (t)x2 )). (5 points). Is the...
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