Homework Answers
Answer:
Here Z(t)= Kt is random process and K is random variable so t is fixed. Mean can be computed using following equation,
Autocovariance:
This is not wide sense stationary process because autocovariance function is not of the form
A process is wide sense stationary if
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ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K...
Please answer all the questions thank you ne 10. 2019 4. A random process Z(t) is...
Please answer all the questions thank you
ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K is a random variable The probability dessity function for K is given below. Use this information to answer the questions below (20 points k <-1 0 fK(k)=-k-1sks k> 1 0 (a) Find the mean function for Z(t). (b) Find the autocovariance function for Z(e). (c) Is this process wide sense stationary (WSS)? Explain your answer in 2-3...
A. For each of the following randomn processes, state whether it is wide-sense stationary (WSS) and why in 1-3 Sente...
A. For each of the following randomn processes, state whether it is wide-sense stationary (WSS) and why in 1-3 Sentences (a) A Poisson random process N(t) with mean function mN () =M and autocovariance function CN(t,t2) = Ati. (b) A Gaussian random process W (t) with mean function mw (t) = 3t and autocovariance function Cw (l,t,) = 9e 2t2 0 and antocorrelation function (c) An exponential random process Z(t) with mean function mz(1) RZ(t1,t2) = e 42 Ll
A....
A random process has a sample function of the form: Where: Y and are constants (NOT...
A random process has a sample function of the form: Where: Y and are constants (NOT random variables) and is a random variable that is uniformly distributed between 0 and . Find: the mean value, the mean square value and variance of Show that the random process is wide-sense-stationary (wss) and its auto correlation depends only on which is the difference in time between and foe a give waveform
A(t) is a wide-sense stationary random process and is a random variable distributed uniformly over [0,...
A(t) is a wide-sense stationary random process and is a random variable distributed uniformly over [0, 211]. Furthermore, is independent of A(t). Three random processes X(t), Y(t), and Z(t) are given by X(t) = A(t) cos(20ft + 0) Y(t) = A(t) cos(507t + 0) z(t) = X(t) + y(t) a. Show that X(t) and Y(t) are stationary in the wide sense. b. Show that Z(t) is not stationary in the wide sense.
Consider two random processes X(t) and Y(t) defined as X(t)=Acos(wot+z), Y(t)=Bsin(wo+z) where A and B and...
Consider two random processes X(t) and Y(t) defined as X(t)=Acos(wot+z), Y(t)=Bsin(wo+z) where A and B and wo are constants and z is a random variable that is uniformly distributed between 0 and 2pi. find the cross-correlation function of X(t) and Y(t). If both X(t) and Y(t) were wide sense stationary , could they also be jointly wide sense stationary?
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...
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?
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)
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...
Stochastic Signal Theory 1. The random variable A is Gaussian distributed with mean 10 and standard...
Stochastic Signal Theory 1. The random variable A is Gaussian distributed with mean 10 and standard deviation e20 A random process X (t) is a function of A defined by the given equation. Use this information to answer the questions below. (24 points) X(t)- Ae'cos(t) (a) Find the mean function for X(t). (b) Find the variance function for X(t). (c) Find the autocovariance function for X (t).
Stochastic Signal Theory 1. The random variable A is Gaussian distributed with mean...
Please answer all the questions thank you
ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K is a random variable The probability dessity function for K is given below. Use this information to answer the questions below (20 points k <-1 0 fK(k)=-k-1sks k> 1 0 (a) Find the mean function for Z(t). (b) Find the autocovariance function for Z(e). (c) Is this process wide sense stationary (WSS)? Explain your answer in 2-3...
A. For each of the following randomn processes, state whether it is wide-sense stationary (WSS) and why in 1-3 Sentences (a) A Poisson random process N(t) with mean function mN () =M and autocovariance function CN(t,t2) = Ati. (b) A Gaussian random process W (t) with mean function mw (t) = 3t and autocovariance function Cw (l,t,) = 9e 2t2 0 and antocorrelation function (c) An exponential random process Z(t) with mean function mz(1) RZ(t1,t2) = e 42 Ll
A....
A(t) is a wide-sense stationary random process and is a random variable distributed uniformly over [0, 211]. Furthermore, is independent of A(t). Three random processes X(t), Y(t), and Z(t) are given by X(t) = A(t) cos(20ft + 0) Y(t) = A(t) cos(507t + 0) z(t) = X(t) + y(t) a. Show that X(t) and Y(t) are stationary in the wide sense. b. Show that Z(t) is not stationary in the wide sense.
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...
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?
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)
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...
Stochastic Signal Theory 1. The random variable A is Gaussian distributed with mean 10 and standard deviation e20 A random process X (t) is a function of A defined by the given equation. Use this information to answer the questions below. (24 points) X(t)- Ae'cos(t) (a) Find the mean function for X(t). (b) Find the variance function for X(t). (c) Find the autocovariance function for X (t).
Stochastic Signal Theory 1. The random variable A is Gaussian distributed with mean...
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