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1. Determine Z-transform including region of convergence a) x(n)=n a" u(-n-1) b) x(n) = {1, 0, -1,0,1, -1) G" for n 2 0 c) x(n) = for n<0 -n

1. Determine Z-transform including region of convergence a) x(n)=n a" u(-n-1) b) x(n) = {1, 0, -1,0,1, -1) G" for n 2 0 c) x(n) = for n<0 -n

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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1. Determine Z-transform including region of convergence a) x(n)=n a" u(-n-1) b) x(n) = {1, 0, -1,0,1, -1) (G)" for n 2 0 n for n<0 c) x(n) = 2. Compute the convolution of the following signals for n20 and X1(n) = * for n<0 (u)n O = (u) x 3. Using long division, determine the inverse z-transform of 1+ 2z-1 X(z) 1- 2z-1 + z-2 4. Determine the causal signal x(n) if its z-transform X(z) is given by: a) X(z) = 1+3z-1 1+3z-1+2z-2 b) X(z) 1-r1+0.5z-2 c) X(z) = 2-15z-1 %3D 1-1.5z-1+0.5z-2z
Transcribed Image Text:1. Determine Z-transform including region of convergence a) x(n)=n a" u(-n-1) b) x(n) = {1, 0, -1,0,1, -1) (G)" for n 2 0 n for n<0 c) x(n) = 2. Compute the convolution of the following signals for n20 and X1(n) = * for n<0 (u)n O = (u) x 3. Using long division, determine the inverse z-transform of 1+ 2z-1 X(z) 1- 2z-1 + z-2 4. Determine the causal signal x(n) if its z-transform X(z) is given by: a) X(z) = 1+3z-1 1+3z-1+2z-2 b) X(z) 1-r1+0.5z-2 c) X(z) = 2-15z-1 %3D 1-1.5z-1+0.5z-2z
6. Determine the response of the system with impulse response h(n)=a" u(n) to the input signal x(n)=u(n)-u(n-10). 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: Im[z) a) x1(n)=x(2-n) 0.5 b)x2(n)=e5* x(n) Re(z) -Oj5 0.5 -0.5 8. We want to design a causal discrete-time LTI system with the property that if the input is x(n) =;)" u(n) -)" u(n - 1) Then the output is y(n) = G)" u(n) Determine the impulse response h(n) and the system function H(z). 9. Consider the causal system y(n) = -a1y(n – 1) + box(n) + b,x(n- 1) Determine: (a) The impulse response (b) The step response (d) The response to the input x(n) = cos(won) 0sn<o
Transcribed Image Text:6. Determine the response of the system with impulse response h(n)=a" u(n) to the input signal x(n)=u(n)-u(n-10). 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: Im[z) a) x1(n)=x(2-n) 0.5 b)x2(n)=e5* x(n) Re(z) -Oj5 0.5 -0.5 8. We want to design a causal discrete-time LTI system with the property that if the input is x(n) =;)" u(n) -)" u(n - 1) Then the output is y(n) = G)" u(n) Determine the impulse response h(n) and the system function H(z). 9. Consider the causal system y(n) = -a1y(n – 1) + box(n) + b,x(n- 1) Determine: (a) The impulse response (b) The step response (d) The response to the input x(n) = cos(won) 0sn<o
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