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A random process X(t) has an autocorrelation function Rxx (T) = 9 + 2e-1| If X(t)...
Please show all work, will rate immediately ?? A random Process XCt) has an auto Correlation...
Please show all work, will rate immediately ??
A random Process XCt) has an auto Correlation function Rxx (T) = 9+2e 121 a) find the mean of Xct) b) If X(+) is the input to a system having an impulse response h(t)= e Btult) (Where is positive), find the mean value of the output process
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?
2. Let Y(t) = (x(0)+)(\pi) where X(t) is a Poisson process with autocorrelation function Rxx(t1, tz)...
2. Let Y(t) = (x(0)+)(\pi) where X(t) is a Poisson process with autocorrelation function Rxx(t1, tz) = tīta + min(tı, tz), and 6 ~ U(0,2%) is independent of X(t). a. Is X(t) W.S.S.? b. If so, find its power spectral density. [25]
2. Let Y(t) = ei(x(0)+o)(\pi) where X(t) is a Poisson process with autocorrelation function Rxx(t1, tz)...
2. Let Y(t) = ei(x(0)+o)(\pi) where X(t) is a Poisson process with autocorrelation function Rxx(t1, tz) = tīta + min(tı, tz), and 6 ~ U(0,2") is independent of X(t). a. Is Y(t) W.S.S.? b. If so, find its power spectral density. [25]
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...
OLUN An ergodic random process X(T) has the following autocorrelation function: Rx(T) = 36+ 1+67² Determine...
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.
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the...
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function of Y(t)
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function...
8.2-24. A random process X(t) is applied to a network with impulse response h(t) = u(t)texp(-bt)...
8.2-24. A random process X(t) is applied to a network with impulse response h(t) = u(t)texp(-bt) where b > 0 is a constant. The cross-correlation of X(t) with the output Y() is known to have the same form: Rxy(t) = u(t)t exp(-bt) (a) Find the autocorrelation of y(t). (b) What is the average power in Y(0)?
Autocorrelation of an X(t) random process is Rxx (t1, t2) = 4e-t-t2 This a Gaussian process...
Autocorrelation of an X(t) random process is Rxx (t1, t2) = 4e-t-t2 This a Gaussian process with mean zero. a) [6p] Is this process wide sense stationary? Briefly explain. b) [9p] Calculate the probability P (X(2)> 1) using the Table at the cover. c) [10p] Calculate approximately the probability P(X(2) > X(4) + 1). Some useful relations 1. Var(X(t)) = E({€)) - (E(X(t))) 2. R(X(t)X(t) = ELX(t-)X(02)]| 3. Var(X(c) +X)) = Var( (t) ) + Var (X (t2) - 2Cov(X...
11.8 A linear system has a transfer function given by H(W) + 15w+50 Determine the power...
11.8 A linear system has a transfer function given by H(W) + 15w+50 Determine the power spectral density of the output when the input function is a. a stationary random process X(t) with an autocorrelation function, Rxx(t)=10e ! b. white noise that has a mean-square value of 1.2 V/Hz
Please show all work, will rate immediately ??
A random Process XCt) has an auto Correlation function Rxx (T) = 9+2e 121 a) find the mean of Xct) b) If X(+) is the input to a system having an impulse response h(t)= e Btult) (Where is positive), find the mean value of the output process
2. Let Y(t) = (x(0)+)(\pi) where X(t) is a Poisson process with autocorrelation function Rxx(t1, tz) = tīta + min(tı, tz), and 6 ~ U(0,2%) is independent of X(t). a. Is X(t) W.S.S.? b. If so, find its power spectral density. [25]
2. Let Y(t) = ei(x(0)+o)(\pi) where X(t) is a Poisson process with autocorrelation function Rxx(t1, tz) = tīta + min(tı, tz), and 6 ~ U(0,2") is independent of X(t). a. Is Y(t) W.S.S.? b. If so, find its power spectral density. [25]
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...
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.
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function of Y(t)
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function...
8.2-24. A random process X(t) is applied to a network with impulse response h(t) = u(t)texp(-bt) where b > 0 is a constant. The cross-correlation of X(t) with the output Y() is known to have the same form: Rxy(t) = u(t)t exp(-bt) (a) Find the autocorrelation of y(t). (b) What is the average power in Y(0)?
Autocorrelation of an X(t) random process is Rxx (t1, t2) = 4e-t-t2 This a Gaussian process with mean zero. a) [6p] Is this process wide sense stationary? Briefly explain. b) [9p] Calculate the probability P (X(2)> 1) using the Table at the cover. c) [10p] Calculate approximately the probability P(X(2) > X(4) + 1). Some useful relations 1. Var(X(t)) = E({€)) - (E(X(t))) 2. R(X(t)X(t) = ELX(t-)X(02)]| 3. Var(X(c) +X)) = Var( (t) ) + Var (X (t2) - 2Cov(X...
11.8 A linear system has a transfer function given by H(W) + 15w+50 Determine the power spectral density of the output when the input function is a. a stationary random process X(t) with an autocorrelation function, Rxx(t)=10e ! b. white noise that has a mean-square value of 1.2 V/Hz
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