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bits enough.Due to little confussion about c bit so i couldn't
solved.If you want to answer for c bit please post it
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process x(t) Question4 (15 points): A random telegraph signal is a taking the values +1 and...
2. (30 points) Let X(t) be a wide-sense stationary (WSS) random signal with power spectral density...
2. (30 points) Let X(t) be a wide-sense stationary (WSS) random signal with power spectral density S(f) = 1011(f/200), and let y(t) be a random process defined by Y(t) = 10 cos(2000nt + 1) where is a uniformly distributed random variable in the interval [ 027]. Assume that X(t) and Y(t) are independent. (a) Derive the mean and autocorrelation function of Y(t). Is Y(t) a WSS process? Why? (b) Define a random signal Z(t) = X(t)Y(t). Determine and sketch the...
A Random Telegraph Signal with rate λ > 0 is a random process X(t) (where for each t, X(t) ∈ {±1}) defined on [0,∞) with the following properties: X(0) = ±1 with probability 0.5 each, and X(t) switches between the two values ±1 at the points of arrival of
A Random Telegraph Signal with rate λ > 0 is a random process X(t) (where for
each t, X(t) ∈ {±1}) defined on [0,∞) with the following properties: X(0) = ±1
with probability 0.5 each, and X(t) switches between the two values ±1 at the
points of arrival of a Poisson process with rate λ i.e., the probability of k changes
in a time interval of length T isP(k sign changes in an interval of length T) = e
−λT...
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...
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...
Q.6 Determine the autocorrelation function and power spectral density of the random process olt)= m(t) cos(21f...
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).
(13 points) The random process X(t) consists of the following two sample functions which are equally...
(13 points) The random process X(t) consists of the following two sample functions which are equally likely: x(t,sı)=e?, x(t,52)=-e 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).
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?
Let x(t) = Acos(27/0t + ?) where fo is a given constant, A is a Rayleigh...
Let x(t) = Acos(27/0t + ?) where fo is a given constant, A is a Rayleigh random variable with ? is a uniformly distributed random variable on [0, 2n, and A and ? are statistically independent. a) Find the mean E[X (t)h b) Find the autocorrelation function E(X(t)X(t+)). c) Is (X(t)) wide-sense stationary? d) Find the power spectral density Sx(f)
The purpose of this assignment is to practice concepts related to the wide-sense stationary processes, filtering,...
The purpose of this assignment is to practice concepts related to the wide-sense stationary processes, filtering, auto-correlation, and power spectral density I. (20 points) Let X(1) denote a wide sense stationary process with μ,-0 and autocorrelation Rdr). Let y(1) = 2 + XUt). What is R)(tz)? Is Y(t) wide sense stationary?
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)....
2. (30 points) Let X(t) be a wide-sense stationary (WSS) random signal with power spectral density S(f) = 1011(f/200), and let y(t) be a random process defined by Y(t) = 10 cos(2000nt + 1) where is a uniformly distributed random variable in the interval [ 027]. Assume that X(t) and Y(t) are independent. (a) Derive the mean and autocorrelation function of Y(t). Is Y(t) a WSS process? Why? (b) Define a random signal Z(t) = X(t)Y(t). Determine and sketch 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...
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...
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).
(13 points) The random process X(t) consists of the following two sample functions which are equally likely: x(t,sı)=e?, x(t,52)=-e 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).
Let x(t) = Acos(27/0t + ?) where fo is a given constant, A is a Rayleigh random variable with ? is a uniformly distributed random variable on [0, 2n, and A and ? are statistically independent. a) Find the mean E[X (t)h b) Find the autocorrelation function E(X(t)X(t+)). c) Is (X(t)) wide-sense stationary? d) Find the power spectral density Sx(f)
The purpose of this assignment is to practice concepts related to the wide-sense stationary processes, filtering, auto-correlation, and power spectral density I. (20 points) Let X(1) denote a wide sense stationary process with μ,-0 and autocorrelation Rdr). Let y(1) = 2 + XUt). What is R)(tz)? Is Y(t) wide sense stationary?
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)....
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