Find X(z) and the region of convergence (ROC) for the signals below, Using Z-transform: 1. x₁[n]= (1/2)" u(n) + (-1/3)¹ u(n) 2. x[n]=(-1/3)^ u(-n-1)+(1/2)n u(-n-1)
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- 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)Evaluate the inverse z-transform of of the functions given below by the three methods described in the text: E(z)=0.5z/(z-1)(z-0.6)
- Q.1 Find the z-transform f(z) and sketch the pole-zero plot with the ROC for each of the following sequences?the following statements given, write if each statement is true or false. a. If the complex frequency domain function, F(s), is derived using a “One-sided” Laplace Transform, the inverse of that function, f(t), is only valid for t ≥ 0. b. When using an ideal transformer, if voltage increases from primary side to secondary side, current also increases from primary side to the secondary side. c. Initial value theorem states that the initial value of a time function f(t) can be obtained from its Laplace Transform F(s) by multiplying the transform by s and letting s approach zero. ..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)
- Determine the causal signal x(n) if its z-transform is given by X(z) = 1+2;-2 %3D 1+z-2Given an RC circuit in Figure 1 is modelled by the differential equation written as, ????+1???(?)=1???(?).If the input, ?(?)=0.8?−??(?) with initial condition ?(0−)=3?, by using the Laplace transform approach determine,a) overall output response, ?(?)b) zero input responsec) zero state responseDetermine the Total Response when x(n)=4(0.5)nu(n)+3(0.75)nu(n) using the Z-transform, given the system described below and its initial conditions.
- Determine the Total Response when x(n)=4(0.5)nu(n)+3(0.75)nu(n) using the Z-transform, given the system described below and its initial conditions.Then considering the given input, what are the energies of the input and the resulting output of the system?y''-4y=e-2t Find the general solution of the second order, constant coefficient, non-homogeneous linear differential equation given below by "Laplace transform"?Find the inverse Laplace transform of the following: 1. X(s) = [s + 2 + 4e^(−3s)]/[(s + 3)(s + 1)] 2. Y(s) = (s + 5)/[(s + 1)(s + 3)] 3. Z(s) = (s^2 + 6s + 7)/(s^2 + 3s + 2), Re(s) > −2 4. W(s) = (s^3 + 2s^2 + 6)/(s^2 + 3s) , Re(s) > 0 5. V (s) = (s^2 + 2s + 5)/[(s + 3)(s + 5)^2), Re(s) > −3 Where ROC is not specified, you may consider all of the s-plane to be ROC.