Show that the following properties hold if X(t) is a WSS process with finite second order...
Let W - {Wi,0< t < ) represent a standard Brownian motion Show that the process Z(s)-(zt-W f.0 < t-1) is a standard Brownian motion, where s > 0 is fixed
QUESTION 14 If (S-1) <0, and (T - G) <0, then (M - X)>0 True False
6.21 For a Poisson process with parameter λ show that for s <r, the correlation between N, and N, is Corr(N,, N)
Consider the following second order PDE Uit – 9Uxx = 0, 0<x< < t > 0, (A) and the following boundary value/initial conditions: Ux(t,0) = uſt, 5) = 0, t>0, u(0, x) = 44(0, x) = 4 cos’ x, 0<x< (BC) (IC) for the function u= u(t, x). a. (5 points) Find ordinary differential equations for functions T = T(t) and X = X(x) such that the function u(t, x) = T(t)X(x) satisfies the PDE (A). b. (5 points) Find...
Q2: Find the complex Fourier series (show your steps) - T < x <07 f(x) 0 < x < Q1: Find the Fourier transform for (show your steps) - 1<x< 0 Otherwise (хе f(x) = { 0,
fx (z)='0 otherwise Let Xa)<...<Xn) be the order statistics. Show that Xa)/X(n) and X(n) are independent random variables.
7. Let h(T) =T,IT <1 (and equal to zero otherwise) be an impulse response function of a WSS process. Find its transfer function (v).
Consider the following. x = sin(t) y = csc(t) 0<t</2 (a) Eliminate the parameter to find a Cartesian equation of the curve. 1 y = X y
3. Given a second-order ODE, [x1,x2] ER?, study the stability of the equilibrium point at the origin. <=x2–2x17x7 + x3) *2=– *1 –2x2(x} + xž)
Consider the following signal t/2+1 -2 <t<0 2(t) = {-t/2+1 0<t<2 elsewhere a) Draw x() b) Draw y(t) = +(2(1 – t)) and show all the intermediate steps in your transformation.