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For the following random process, where fe is called the carrier frequency in Hertz,...
Consider a sinusoidal signal with random phase, defined by x(t)=Acos(2πfct+θ), where A and FC are constant and θ is a random variable uniform distributed over interval [-π,π], that is f(θ)={█(1/2π,&-π≤θ≤π@0,&elsewhere)┤ Describe the autocorrelation RX(τ
Consider a sinusoidal signal with random phase, defined by , where A and FC are constant and is a random variable uniform distributed over interval [-, that isa) Describe the autocorrelation RX of a sinusoidal wave X(t)b) Describe the power spectral density SX of a sinusoidal wave X(t)Consider a sinusoidal signal with random phase, defined by , where A and FC are constant and is a random variable uniform distributed over interval [-, that isa) Describe the autocorrelation RX of...
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)
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. 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...
5. A stationary random process X[n] is input to a discrete time LTI system with frequency...
5. A stationary random process X[n] is input to a discrete time LTI system with frequency response j“)-10 zero mean given as A(e nmay be expressed as where Wnlis a zero mea a-HS1 unit variancei.i.d. (independent identically distributed) Gaussian sequence and c, d are constants. Let Yl be the output random a)Determine the mean function for the output random sequence Yn in terms ofa, c and d b) Determine S7 (e), the power spectral density ofthe output random sequence Yn]...
random vibrations Problem 1 Two random variables x and y have the joint probability density function where c is a...
random vibrations
Problem 1 Two random variables x and y have the joint probability density function where c is a constant. Verify that x and y are statistically independent and find the value of c for plx, y) to be correctly normalized. Check that Elx) Elyl-0 and that Elx2] and Ely') are both infinite Problem 2. Each sample function x(t) of a random process x(t) is given by: where a, a2, wh, and w are constants but 61 and 62,...
i need help on question 3 to 22 please. Midterm ex review. MATH 101 Use the...
i need help on question 3 to 22 please.
Midterm ex review. MATH 101 Use the following information to answer the next four exercises. The midterm grades on a chemistry exam, graded on a scale of 0 to 100, were: 62, 64, 65, 65, 68, 70, 72, 72, 74, 75, 75, 75, 76,78, 78, 81, 82, 83, 84, 85, 87, 88, 92, 95, 98, 98, 100, 100,740 1. Do you see any outliers in this data? If so, how would...
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)
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. 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...
5. A stationary random process X[n] is input to a discrete time LTI system with frequency response j“)-10 zero mean given as A(e nmay be expressed as where Wnlis a zero mea a-HS1 unit variancei.i.d. (independent identically distributed) Gaussian sequence and c, d are constants. Let Yl be the output random a)Determine the mean function for the output random sequence Yn in terms ofa, c and d b) Determine S7 (e), the power spectral density ofthe output random sequence Yn]...
random vibrations
Problem 1 Two random variables x and y have the joint probability density function where c is a constant. Verify that x and y are statistically independent and find the value of c for plx, y) to be correctly normalized. Check that Elx) Elyl-0 and that Elx2] and Ely') are both infinite Problem 2. Each sample function x(t) of a random process x(t) is given by: where a, a2, wh, and w are constants but 61 and 62,...
i need help on question 3 to 22 please.
Midterm ex review. MATH 101 Use the following information to answer the next four exercises. The midterm grades on a chemistry exam, graded on a scale of 0 to 100, were: 62, 64, 65, 65, 68, 70, 72, 72, 74, 75, 75, 75, 76,78, 78, 81, 82, 83, 84, 85, 87, 88, 92, 95, 98, 98, 100, 100,740 1. Do you see any outliers in this data? If so, how would...
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