Consider the random process n(u, t) with t ∈ R, defined by
n(u, t) = ∑ δ(t − nT − θ(u) where ∑ is n=−∞ to ∞
where δ(.) denotes the Dirac delta function and θ(u) is a random variable that uniformly distributed on (−T/2, T/2).
Assume that n(u, t) has a Fourier series expansion, what it is?
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Consider the random process n(u, t) with t ∈ R, defined byn(u, t) = ∑ p(t − nT − θ(u)) where ∑ is n=−∞ to ∞Using the shifting property of delta functions, indicate how you would generate y(u, t) from n(u, t) and p(t).where θ(u) is a random variable that uniformly distributed on (−T/2, T/2).
(10 pts) A random process has sample function of the form x(t) random variable uniformly distributed from 0 to 2π. 2. 2sin(t + θ), where e is Find Rx(τ) EX(t)x(t + τ), Show the derivations and simplify the expression as muc as possible. Write your final result in the box.
Consider a random process where rectangular pulses of width 1 are separated in time by intervals of T seconds The amplitude of each pulse is determined independently and with equal probability to be either 1 0, or -1.Pulses begin at periodic time instants to t nT where to is a random variable that is uniformly distributed over the range O to T. Asample function is shown below. to -T to+ T to +37 to to + 27 to + 4T...
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)....
Assume random variable ? is uniformly distributed in the interval (−?/2 ,?⁄ 2]. Define the random variable ?=tan (?), where tan (∙) denotes the tangent function. Note that the derivative of tan (?) is 1/(cos (?)2) . a) Find the PDF of ?. b) Find the mean of ? .Define the random variable ?=1/?. c) Find the PDF of ?. Assume random variable X is uniformly distributed in the interval (-1/2, 1/2). Define the random variable Y = tan(X), where...
2. Prove the following useful properties of Dirac δ-functions (a) δ(ax) = (z) (b) zfic) =0 (c) f(x)5(-a) f(a)5(r d) δ(z-a (aメ0) a) ( dz9(x-a) ) where θ(x) is the step function defined as 1 if r 0 0 if r <0 θ(z) = 2. Prove the following useful properties of Dirac δ-functions (a) δ(ax) = (z) (b) zfic) =0 (c) f(x)5(-a) f(a)5(r d) δ(z-a (aメ0) a) ( dz9(x-a) ) where θ(x) is the step function defined as 1 if...
In the following, x, (t)-Evenx(i), x,(1)-Odd{x(t): l n20 u(t)- «[n]- δ[n]-(0 otherwise δ(r) is the Dirac delta function
and is X(t) a WSS process? 6.11 Sinusoid with random phase. Consider a random process x(t)-A cos(wot + ?), where wo are nonrandom positive constants and o is a RV uniformly distributed over A and (0, ?), i.e., ? ~11(0, ?). (a) Find the mean function 2(t) of X(t).
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...
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks 3. Consider the function defined by...