A stochastic process X() is defined by where A is a Gaussian-distributed random variable of zero ...
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 solve this. 8.18 A discrete random process is defined by where φ is a uniform rndom variable in the range of-π to π. (a) Sketch a typical sample function of X b) Are its mean and variance constants (i.e., independent of k)7 (e) Is X Je] stationary (d) Is it mean ergodic? 8.18 A discrete random process is defined by where φ is a uniform rndom variable in the range of-π to π. (a) Sketch a typical sample function...
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...
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)....
The random process X(t) is defined by X(t) = X cos 27 fot + Y sin 2 fot, where X and Y are two zero-mean Gaussian random variables, each with the variance 02. (a) Find ux(t) (b) Find RX(T). Is X(t) stationary? (c) Repeat (a) and (b) for 0 + 0
The input to a system is a Gaussian random variable below X with zero mean and variance of σ- as shown x System The output of the system is a random variable Y given as follows: -a b, X>a (a) Determine the probability density function of the output Y (b) Now assume that the following random variable is an input to the system at time t: where the amplitude A is a constant and phase s uniformly distributed over (0,2T)....
blem 4 , The input to a system is a Gaussian random variable below X with zero mean and variance of σ as shown System The output of the system is a random variable Y given as follows: bX (a) Determine the probability density function of the output Y b) Now assume that the following random variable is an input to the system at time t: where the amplitude A is a constant and phase θ is uniformly distributed over...
X is a Gaussian random variable with zero mean and variance ơ2 This random variable 5 20 points is passed through a quantizer device whose input-output relation is g(z) = Zn, for an x < an+1, 1 N where In lies in the interval [an, Qn+1) and the sequence fa, a2, al z-00, aN41 # oo, and for i > j we have ai > aj. Find the PMF of the output random variable Y g(X). aN+1) satisfies the conditions
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...
Let a random process x(t) be defined by x(t) = At + B (a) If B is a constant and A is uniformly distributed between-1 and +1, sketch a few sample functions (b) If A is a constant and B is uniformly distributed between 0 and 2, sketch a few sample functions c) Evaluate (r2(t)) d) Evaluate x2(t) e) Using the results of part c) and d), determine whether the process is ergodic for the averages Let a random process...