4.(a) For the discrete-time signal given byx[n] = (1/6)*u[n-2](i)Using the Z-transform definition, find its Z-transform,X(z).(ii)Plot the pole/zero diagram, shading the ROC.(b) For the two systems with impulse responseshi[n] = (0.5)" u[n]h2[n] = (2)ªu[n]Write down their transfer functions, H1(z) and H2(z).Don't forget to include the corresponding ROCS.and(i)If we connect H1(z) and H2(z) in cascade, the resultingcascade interconnection will have a combined transferfunction calculated by(ii)H(z) = H1(z).H2(z), Determine the transfer functioninterconnection of the two systems for the specific valuesof H1(z) and H2(z) given in part (b)(i) above. Find all thepoles and zeros for the cascade system and indicate themon the pole-zero plot shading the ROC.for acascade

We are advised to answer first part only. As you have not mentioned which part to answer. So, we are…

Answered: (a) For the discrete-time signal given…

(a) For the discrete-time signal given by x[n] = (1/6)"u[n-2] (i) Using the Z-transform definition, find its Z-transform, X(z). (ii) Plot the pole/zero diagram, shading the ROC. 4.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

4.
(a) For the discrete-time signal given by
x[n] = (1/6)*u[n-2]
(i)
Using the Z-transform definition, find its Z-transform,
X(z).
(ii)
Plot the pole/zero diagram, shading the ROC.
(b) For the two systems with impulse responses
hi[n] = (0.5)" u[n]
h2[n] = (2)ªu[n]
Write down their transfer functions, H1(z) and H2(z).
Don't forget to include the corresponding ROCS.
and
(i)
If we connect H1(z) and H2(z) in cascade, the resulting
cascade interconnection will have a combined transfer
function calculated by
(ii)
H(z) = H1(z).H2(z),

Determine the transfer function
interconnection of the two systems for the specific values
of H1(z) and H2(z) given in part (b)(i) above. Find all the
poles and zeros for the cascade system and indicate them
on the pole-zero plot shading the ROC.
for a
cascade

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