Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Analog to Digital Converters
The analog-to-digital converter (ADC) allows circuits controlled by microprocessors, Arduinos, Raspberry Pi, and various reasonable digital circuits to be connected to the real world. In the real world, analog signals have a continuous stream of informat…
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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.
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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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