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Consider the following difference equation and excitation: y[n] 1.5y[n-1] +0.5y[n = 2] = 1[n]; 1, n = 1 x[n] = 0, otherwise. Assume zero initial conditions, namely, y[-1] = y[−2] = 0. (a) Find y[n], using the z-transform. (b) Verify the value of y[0] in part (a), using the initial-value property. (c) Will the final-value property give the correct value of y[oo]? If your answer is yes, find the final value. Otherwise, state why the final-value property is not applicable.

Consider the following difference equation and excitation: y[n] 1.5y[n-1] +0.5y[n = 2] = 1[n]; 1, n = 1 x[n] = 0, otherwise. Assume zero initial conditions, namely, y[-1] = y[−2] = 0. (a) Find y[n], using the z-transform. (b) Verify the value of y[0] in part (a), using the initial-value property. (c) Will the final-value property give the correct value of y[oo]? If your answer is yes, find the final value. Otherwise, state why the final-value property is not applicable.

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the following difference equation and excitation: y[n] 1.5y[n-1] +0.5y[n = 2] = 1[n]; 1, n = 1 x[n] = 0, otherwise. Assume zero initial conditions, namely, y[-1] = y[−2] = 0. (a) Find y[n], using the z-transform. (b) Verify the value of y[0] in part (a), using the initial-value property. (c) Will the final-value property give the correct value of y[oo]? If your answer is yes, find the final value. Otherwise, state why the final-value property is not applicable.
Transcribed Image Text:Consider the following difference equation and excitation: y[n] 1.5y[n-1] +0.5y[n = 2] = 1[n]; 1, n = 1 x[n] = 0, otherwise. Assume zero initial conditions, namely, y[-1] = y[−2] = 0. (a) Find y[n], using the z-transform. (b) Verify the value of y[0] in part (a), using the initial-value property. (c) Will the final-value property give the correct value of y[oo]? If your answer is yes, find the final value. Otherwise, state why the final-value property is not applicable.
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