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)
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Author:Robert L. Boylestad
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4e23d50-b6e1-4880-9ad9-a789799b751b%2Fc5d7b512-b74a-4038-bd86-9b1e8cbbe768%2F9e2y08_processed.png&w=3840&q=75)
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.
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Given:
A LTI system described by the difference equation,
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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