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Problem 1 A causal LTI system H is described by the following transfer function: 1+ 2z-1 + z-2 H(z) 1+ 4z-1+ 4z¬2 (a) Give pole-zero plot of the system and indicate its ROC. (b) Using inverse Z-transform, compute the impulse response h[n] of the system H. (c) What is the difference equation relating input x[n] and output y[n] of system H? (d) Is the system stable?

Problem 1 A causal LTI system H is described by the following transfer function: 1+ 2z-1 + z-2 H(z) 1+ 4z-1+ 4z¬2 (a) Give pole-zero plot of the system and indicate its ROC. (b) Using inverse Z-transform, compute the impulse response h[n] of the system H. (c) What is the difference equation relating input x[n] and output y[n] of system H? (d) Is the system stable?

Introductory Circuit Analysis (13th Edition)
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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Problem 1 A causal LTI system H is described by the following transfer function: 1+ 2z-1 + z-2 H(z): %D 1+4z-1 + 4z-2 (a) Give pole-zero plot of the system and indicate its ROC. (b) Using inverse Z-transform, compute the impulse response h[n] of the system H. (c) What is the difference equation relating input x[n] and output y[n] of system H? (d) Is the system stable?
Transcribed Image Text:Problem 1 A causal LTI system H is described by the following transfer function: 1+ 2z-1 + z-2 H(z): %D 1+4z-1 + 4z-2 (a) Give pole-zero plot of the system and indicate its ROC. (b) Using inverse Z-transform, compute the impulse response h[n] of the system H. (c) What is the difference equation relating input x[n] and output y[n] of system H? (d) Is the system stable?
Problem 2 Draw the following structures for the system H(z) in Problem 1. (a) Direct Form I, II (b) Transpose Direct Form II
Transcribed Image Text:Problem 2 Draw the following structures for the system H(z) in Problem 1. (a) Direct Form I, II (b) Transpose Direct Form II
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