We are given the following five facts about a real signal x(t) with Laplace transform X(s): 1. X(s) has exactly two poles. 2. X(s) has no zeros in the finite s-plane. 3. X(s) has a pole at s = -1 + j. 4. e2¹ x() is not absolutely integrable. 5. X(0) = 8. Determine X(s) and specify its region of convergence.

Find the inverse z-transform of the function F(2) (z+ 0.1)(z+0.2)(z+ 0.3)

1. (a) Using the definition, find X(z), the z-transform of the signal. x[n] = 2"u[n-1] (b) Draw the pole/zero diagram and shade its ROC.

Part a & b

Dear, {..} Do part C only please

need help with this hw problem..thanks !

find the inverse z transform of x(z)=(z-1)(z+0.8)/(z-0.5)(z+0.2)

Q1 Find the z transform for each of the following sequences: a) 3u(n-4) b) 2(-0.5)nu(n) c) 4e-2nu(n) d) 4(0.8) "cos (0.1лn)u(n) Q2 Given the two sequences x₁(n)= -28(n)+58(n-2) and x2(n)= 48(n-4) a) Let x3(n) = x₁(n) * x2 (n) Determine the Z transform of x3(n) b) Find x3(n) using the inverse transform of X3(z). Q3 Using the Z-transform properties and the Z-transform table find the inverse Z- transform for each of the following sequences a) 5- (7z/z+1) - (3z/z-0.5) b) (-3z/(z-0.5)) +[ 8z/(z−0.8)]+ [2z/(z-0.8)²] c) 3z/(z²+1.414z+1) d) (5z %/z-1)-[ z^²/(z−1)²] + [z −¹⁰0] + [z ³/z-0.75] Q4 Use partial fraction expansion, Find the inverse Z-transform of the following: a) [1/(z²+0.5z+0.06)] b) z/[(z+0.3)(z-0.5)] c) 5z/[(z-0.75) (z²-z+0.5)] d) 2z(z-0.4)/[(z-0.2)²(z+0.8)] Q5 A system is described by the following difference equation y(n)-0.5y(n-1) +0.06y(n-2)= (0.4)n-1u(n-1) Determine the solution when the initial conditions are y(-1) = 1 and y(-2)=2.

7. Consider the z-transform of a discrete-time signal x[n] given as follows: 2-¹ (1-12-²) 4 -1 (1-2 +22-²)(1-z-¹) X(z) = (a) Plot the zeros and poles on the z-plane, specify whether or not 0 and ∞ are zeros or poles, and show the possible choices of the ROC. (b) Determine the inverse z-transform x[n] if we know that the discrete-time Fourier transform exists.

7. Let x(n) be a causal sequence with z-transform X(z) whose pole-zero plot is shown below. Sketch the pole-zero plots and the ROC of the following sequence: a) x1(n)=x(2-n) Im(z) b)x2(n)=e5* x(n) 0.5 Re(z) -0:5 -1 0.5 -0.5