Suppose that the z-transform of x[n] is 1 X(z) = (1 + 4z-2)(1+3z-¹) Sketch all possible ROC corresponding to X(z).
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- y''-4y=e-2t Find the general solution of the second order, constant coefficient, non-homogeneous linear differential equation given below by "Laplace transform"?Problem 1. Which gives the Laplace transforms of the given time-domain function? Let a = 2 pi - 2arctan (s/6) pi - 2arctan (2s/3) pi - 2arctan (s/3) (1/2)pi - 2arctan (s/3)Find the expression X (z), which is the Z transformation of the given sign x [n]. Zeros of x (z) andIdentify the poles. What can be said about meeting the stability criterion?
- Problem 4. Which gives the Laplace transforms of the given time-domain function? 1.5 ln [(s^2 + 142129)/s^2] 1.5 ln [(s^2 - 142129)/s^2] -1.5 ln [(s^2 - 142129)/s^2] -1.5 ln [(s^2 + 142129)/s^2]Consider a discrete-time system given by H(z) = (1 - (½)z)(1-(1/5)z) / (z-½)(z-1/5). -Find the frequency response of this system, and show why it is special. -Find the steady-state response to x[n] = cos n (do not use z transforms)Why is the z Transform of n*U[n] = z /(z-1)^2? What is the z Transform of n^2 *U[n]?