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Consider a discrete time system given by y[n] + ay[n – 1] = x[n] + bx[n – 1] + x[n – 2] If x[n] = COS + cos determine the constants a and b so that the output is y[n]: 3 = - sin (n + 0). Also, what is the resulting phase 0? 4

Consider a discrete time system given by y[n] + ay[n – 1] = x[n] + bx[n – 1] + x[n – 2] If x[n] = COS + cos determine the constants a and b so that the output is y[n]: 3 = - sin (n + 0). Also, what is the resulting phase 0? 4

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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Please solve using convolution without the Laplace transform. 

Consider a discrete time system given by \[ y[n] + a y[n-1] = x[n] + b x[n-1] + x[n-2] \] If \( x[n] = \cos\left(\frac{2\pi}{3} n\right) + \cos\left(\frac{\pi}{2} n\right) \), determine the constants \( a \) and \( b \) so that the output is \[ y[n] = \frac{3}{4} \sin\left(\frac{\pi}{2} n + \theta\right) \]. Also, what is the resulting phase \(\theta\)?
Transcribed Image Text:Consider a discrete time system given by \[ y[n] + a y[n-1] = x[n] + b x[n-1] + x[n-2] \] If \( x[n] = \cos\left(\frac{2\pi}{3} n\right) + \cos\left(\frac{\pi}{2} n\right) \), determine the constants \( a \) and \( b \) so that the output is \[ y[n] = \frac{3}{4} \sin\left(\frac{\pi}{2} n + \theta\right) \]. Also, what is the resulting phase \(\theta\)?
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