Question 2 (a) Determine the z-transform, including the ROC in z-plane and a sketch of the pole-zero-plot, for sequence: x[»]= a"u[] (b) ) For the z-transform H(z) = 1/ (1 – 4z)( 1 /4 – V3 /2z + z?) 2 Determine possible regions of convergence. In each case comment stability and causality of the system whose transfer function is H(z). What is the output of the stable system to the input x(n) = 2cos(nt/2)? (c) A causal discrete-time signal x(n) has the Fourier transform X(e"). Write its z-transform in terms of the Fourier transform of the discrete-time signal, i.e., write the z-transform value based on its values on the unit circle.

Question 2 (a) Determine the z-transform, including the ROC in z-plane and a sketch of the pole-zero-plot, for sequence: x[»]= a"u[] (b) ) For the z-transform H(z) = 1/ (1 – 4z)( 1 /4 – V3 /2z + z?) 2 Determine possible regions of convergence. In each case comment stability and causality of the system whose transfer function is H(z). What is the output of the stable system to the input x(n) = 2cos(nt/2)? (c) A causal discrete-time signal x(n) has the Fourier transform X(e"). Write its z-transform in terms of the Fourier transform of the discrete-time signal, i.e., write the z-transform value based on its values on the unit circle.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.5P

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4:16 ull 3G O A moodle.nct.edu.om P Flag question For a STABLE LTI system, all the poles of the system function H(z) must lie inside the unit circle. Select one: True False Question Not yet answered Marked out of 1.00 P Flag question The z-transform of x[n]=6(n-3) is X(z)=Z³ O TRUE O FALSE Question 3 Not yet answered Markod out of 1 00 II
Z-Transform and Inverse Z-Transform
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