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7. Consider the z-transform of a discrete-time signal x[n] given as follows: 2-¹ (1-12-²) 9 (1-z-¹ +22-²)(1 – 2−¹) X(z) = (a) Plot the zeros and poles on the z-plane, specify whether or not 0 and ∞ are zeros or poles, and show the possible choices of the ROC. (b) Determine the inverse z-transform x[n] if we know that the discrete-time Fourier transform exists.

7. Consider the z-transform of a discrete-time signal x[n] given as follows: 2-¹ (1-12-²) 9 (1-z-¹ +22-²)(1 – 2−¹) X(z) = (a) Plot the zeros and poles on the z-plane, specify whether or not 0 and ∞ are zeros or poles, and show the possible choices of the ROC. (b) Determine the inverse z-transform x[n] if we know that the discrete-time Fourier transform exists.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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7. Consider the z-transform of a discrete-time signal x[n] given as follows: 2-¹ (1-12-²) 4 -1 (1-2 +22-²)(1-z-¹) X(z) = (a) Plot the zeros and poles on the z-plane, specify whether or not 0 and ∞ are zeros or poles, and show the possible choices of the ROC. (b) Determine the inverse z-transform x[n] if we know that the discrete-time Fourier transform exists.
Transcribed Image Text:7. Consider the z-transform of a discrete-time signal x[n] given as follows: 2-¹ (1-12-²) 4 -1 (1-2 +22-²)(1-z-¹) X(z) = (a) Plot the zeros and poles on the z-plane, specify whether or not 0 and ∞ are zeros or poles, and show the possible choices of the ROC. (b) Determine the inverse z-transform x[n] if we know that the discrete-time Fourier transform exists.
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