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Problem 4. Given the Linear Difference Equation y[n]=0.5y[n-1]+2x[n–1] Determine the output sequence for each of the following inputs. In each case the final answer y[n] has to be a real signal (nothing complex): Ql: x[n] = 2cos(0.5zn)u[n] ; Q2. x[n]= 2cos(0.5zn) Q3: x[n]= 2 cos (0.5zn)u[=n-1]

Problem 4. Given the Linear Difference Equation y[n]=0.5y[n-1]+2x[n–1] Determine the output sequence for each of the following inputs. In each case the final answer y[n] has to be a real signal (nothing complex): Ql: x[n] = 2cos(0.5zn)u[n] ; Q2. x[n]= 2cos(0.5zn) Q3: x[n]= 2 cos (0.5zn)u[=n-1]

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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### Problem 4. Given the Linear Difference Equation \[ y[n] = 0.5 y[n-1] + 2 x[n-1] \] Determine the output sequence for each of the following inputs. In each case the final answer \( y[n] \) has to be a real signal (**nothing complex**): **Q1:** \( x[n] = 2 \cos(0.5\pi n)u[n] \) **Q2:** \( x[n] = 2 \cos(0.5\pi n) \) **Q3:** \( x[n] = 2 \cos(0.5\pi n) u[-n-1] \) For educational purposes, this problem examines your understanding of solving linear difference equations and determining output sequences for given inputs. Make sure to derive real-valued signals for the final outputs.
Transcribed Image Text:### Problem 4. Given the Linear Difference Equation \[ y[n] = 0.5 y[n-1] + 2 x[n-1] \] Determine the output sequence for each of the following inputs. In each case the final answer \( y[n] \) has to be a real signal (**nothing complex**): **Q1:** \( x[n] = 2 \cos(0.5\pi n)u[n] \) **Q2:** \( x[n] = 2 \cos(0.5\pi n) \) **Q3:** \( x[n] = 2 \cos(0.5\pi n) u[-n-1] \) For educational purposes, this problem examines your understanding of solving linear difference equations and determining output sequences for given inputs. Make sure to derive real-valued signals for the final outputs.
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