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Exercise 8: A linear time-invariant system is described by the difference equation y[n] = 2x[n] + 4x[n − 1] − 3x[n − 2] + 3x[n − 3] — 4x[n − 4] − 2x [n - 5] a) Write a simple formula for the magnitude of the frequency response |H(ej^)|. Take advantage of the odd symmetry of the filter coefficients (i.e., bo = -b5, b₁ -b4, etc.) to express your answer in terms of real-valued functions only. b) Derive a simple formula for the phase of the frequency response ZH(ej). c) Determine the impulse response h[n], and plot h[n] as a function of n.

Exercise 8: A linear time-invariant system is described by the difference equation y[n] = 2x[n] + 4x[n − 1] − 3x[n − 2] + 3x[n − 3] — 4x[n − 4] − 2x [n - 5] a) Write a simple formula for the magnitude of the frequency response |H(ej^)|. Take advantage of the odd symmetry of the filter coefficients (i.e., bo = -b5, b₁ -b4, etc.) to express your answer in terms of real-valued functions only. b) Derive a simple formula for the phase of the frequency response ZH(ej). c) Determine the impulse response h[n], and plot h[n] as a function of n.

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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Exercise 8: A linear time-invariant system is described by the difference equation y[n] = 2x[n] + 4x[n − 1] − 3x[n − 2] + 3x[n − 3] − 4x[n − 4] − 2x[n − 5] - a) Write a simple formula for the magnitude of the frequency response |H(ej@)|. Take advantage of the odd symmetry of the filter coefficients (i.e., bo = -b5, b₁ -b4, etc.) to express your answer in terms of real-valued functions only. = b) Derive a simple formula for the phase of the frequency response <H(ej®). c) Determine the impulse response h[n], and plot h[n] as a function of n.
Transcribed Image Text:Exercise 8: A linear time-invariant system is described by the difference equation y[n] = 2x[n] + 4x[n − 1] − 3x[n − 2] + 3x[n − 3] − 4x[n − 4] − 2x[n − 5] - a) Write a simple formula for the magnitude of the frequency response |H(ej@)|. Take advantage of the odd symmetry of the filter coefficients (i.e., bo = -b5, b₁ -b4, etc.) to express your answer in terms of real-valued functions only. = b) Derive a simple formula for the phase of the frequency response <H(ej®). c) Determine the impulse response h[n], and plot h[n] as a function of n.
Expert Solution
Step 1

Given:

A LTI system described by the difference equation, 

y[n]=2x[n]+4x[n-1]-3x[n-2]+3x[n-3]-4x[n-4]-2x[n-5],

To find:

a) Magnitude of the frequency response, 

b) Phase of the frequency response, 

c) Impulse response h[n] and plot h[n] as a function of n.

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