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![Autocorrelation function of X, Ry(t), t2) E[(X+, - M.)(Xt2 - Mt2)] σι,σι2 E[X4,X2] e-21-22 0.5 * 0122X., da, dx2 +0.5 0112Xqd](http://img.homeworklib.com/questions/b082ebd0-e940-11ea-b4a8-43bdf55781e6.png?x-oss-process=image/resize,w_560)
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(13 points) The random process X(t) consists of the following two sample functions which are equally...
Can someone please explain how to solve the problem below? I keep getting the answer incorrect....
Can someone please explain how to solve the problem below? I
keep getting the answer incorrect.
(13 points) The random process X(t) consists of the following two sample functions which are equally likely: x(t,sı)=e", x(t,82)=-et Determine the mean and autocorrelation function of X(t), and also determine whether X(t) is wide sense stationary. (Note: no credit will be awarded for correct guesses without justification).
process x(t) Question4 (15 points): A random telegraph signal is a taking the values +1 and...
process x(t) Question4 (15 points): A random telegraph signal is a taking the values +1 and -1 as f+1 1-1 wheret,is a set of Poisson points with average density a) Determine the mean and autocorrelation of x(t). b) Judge whether x(t) is Wide Sense Stationary, why? c) Determine the Power Spectral Density S(w) of 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?
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?
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...
5. Let X(t) be a random process which consist of the summation of two sinusoidal components...
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...
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...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to...
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...
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)....
t + τ Proof From Definition 10.17, RİT (r) yields Rn(t) = Elx()r(t + τ)]. Making the substitution u Since X(0) and Y(O) are jointly wide sense stationary, Ryr(u, -t for random sequences Rx-r). The...
t + τ Proof From Definition 10.17, RİT (r) yields Rn(t) = Elx()r(t + τ)]. Making the substitution u Since X(0) and Y(O) are jointly wide sense stationary, Ryr(u, -t for random sequences Rx-r). The proof is similar i: 10.11X(t) is a wide sense stationary stochastic process with autocorrelation function Rx(r). (2) Express the autocorrelation function of Y(C) in terms of Rx(r) Is r) wide sense (2) Express the cross-correlation function of x(t) and Y (t) in terms of Rx(t)...
Can someone please explain how to solve the problem below? I
keep getting the answer incorrect.
(13 points) The random process X(t) consists of the following two sample functions which are equally likely: x(t,sı)=e", x(t,82)=-et Determine the mean and autocorrelation function of X(t), and also determine whether X(t) is wide sense stationary. (Note: no credit will be awarded for correct guesses without justification).
process x(t) Question4 (15 points): A random telegraph signal is a taking the values +1 and -1 as f+1 1-1 wheret,is a set of Poisson points with average density a) Determine the mean and autocorrelation of x(t). b) Judge whether x(t) is Wide Sense Stationary, why? c) Determine the Power Spectral Density S(w) of x(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?
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...
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...
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...
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...
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)....
t + τ Proof From Definition 10.17, RİT (r) yields Rn(t) = Elx()r(t + τ)]. Making the substitution u Since X(0) and Y(O) are jointly wide sense stationary, Ryr(u, -t for random sequences Rx-r). The proof is similar i: 10.11X(t) is a wide sense stationary stochastic process with autocorrelation function Rx(r). (2) Express the autocorrelation function of Y(C) in terms of Rx(r) Is r) wide sense (2) Express the cross-correlation function of x(t) and Y (t) in terms of Rx(t)...
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