Q1. A causal discrete-time system is characterized by the difference equation: Уn] %3D у[п - 2] + x[n] — х[п — 4]. a. Find the transfer function, H(z), of this system. (Hint: (x* – 1) = (x – 1)(x + 1)(x – j)(x + j)) b. Plot the pole-zero diagram and clearly mention the ROC for H(z). c. Show that the system is unstable by specifying a bounded input, x[n], for which this system results in unbounded output.
Q1. A causal discrete-time system is characterized by the difference equation: Уn] %3D у[п - 2] + x[n] — х[п — 4]. a. Find the transfer function, H(z), of this system. (Hint: (x* – 1) = (x – 1)(x + 1)(x – j)(x + j)) b. Plot the pole-zero diagram and clearly mention the ROC for H(z). c. Show that the system is unstable by specifying a bounded input, x[n], for which this system results in unbounded output.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![Q1. A causal discrete-time system is characterized by the difference equation:
У'п] %3D у[п — 2] + x[п] — х[п — 4].
a. Find the transfer function, H(z), of this system. (Hint: (x* – 1) = (x – 1)(x +
1)(x – j)(x + j))
b. Plot the pole-zero diagram and clearly mention the ROC for H(z).
c. Show that the system is unstable by specifying a bounded input, x[n], for which
this system results in unbounded output.
d. Sketch the magnitude of the frequency response, |H(w)| from –n <w< T.
e. Find a closed form expression for the output when the input is given as x[n] =
2 cos (n) + 3cos(Tn)
f. Find the impulse response, h[n], of the discrete-time system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f573fa6-080c-4dbe-8078-6e2e236dbf6d%2F214ecc66-5e56-4a13-9252-03876c2d48a9%2F9rt6xo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1. A causal discrete-time system is characterized by the difference equation:
У'п] %3D у[п — 2] + x[п] — х[п — 4].
a. Find the transfer function, H(z), of this system. (Hint: (x* – 1) = (x – 1)(x +
1)(x – j)(x + j))
b. Plot the pole-zero diagram and clearly mention the ROC for H(z).
c. Show that the system is unstable by specifying a bounded input, x[n], for which
this system results in unbounded output.
d. Sketch the magnitude of the frequency response, |H(w)| from –n <w< T.
e. Find a closed form expression for the output when the input is given as x[n] =
2 cos (n) + 3cos(Tn)
f. Find the impulse response, h[n], of the discrete-time system.
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