Answered: For the causal discrete-time LTI system…

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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For the causal discrete-time LTI system implemented using the
difference equation y[n] =-0.25y[n-1]+0.15y[n-2]+4x[n]+0,25x[n-1] where x[n] is the input signal, and y[n] is the output signal.

a) Draw the direct form-II block diagram of the system.

b) Find the transfer function of the system, H(z).

c) Sketch the pole-zero diagram and indicate the ROC. Determine if the Fourier
transform of the system H(e^jw) exists. If the Fourier transform exists, write H(e^jw).

For the causal discrete-time LTI system implemented using the
difference equation
уm] 3 -0.25у (n — 1] + 0.125y(n — 2] + 4г(n] + 0.25x (n — 1]
where a[n] is the input signal, and y[n] is the output signal.
а.
Draw the direct form-II block diagram of the system.
b.
Find the transfer function of the system, H(2).
Sketch the pole-zero diagram and indicate the ROC. Determine if the Fourier
transform of the system H(ew) exists. If the Fourier transform exists, write H(ej").
с.
d.
u-п — 1).
Find the z-transform of the output, Y(2), when the input is x[n]
Specify the ROC for Y(z).
Z-Transform Definition : X(z) 4 ) x[n]z¯"
n=-00

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