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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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![**Discrete-Time Signal Processing Quiz**
**Question:**
Select the correct expression for \( x[n] \) where:
\[ X(e^{j\omega}) =
\begin{cases}
4 & \text{for } 0 < \omega \leq \pi \\
0 & \text{Otherwise}
\end{cases}
\]
**Options:**
1. \( \dfrac{4}{j2\pi n} \left( e^{-j\pi n} - 1 \right) \)
2. \( \dfrac{4}{j2\pi n} \left( e^{j\pi n} + 1 \right) \)
3. \( \dfrac{4}{j2\pi n} \left( e^{j\pi n} - 1 \right) \)
4. \( \dfrac{4}{j2\pi n} \left( e^{+j \pi n} + 1 \right) \)
**Explanation of Options:**
Each option represents a different Fourier inverse transform expression, which is used to determine the time-domain sequence \(x[n]\) from the frequency-domain representation \(X(e^{j \omega})\). The correct expression must satisfy the given condition for \(X(e^{j \omega})\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9de2b0ed-01a2-4a8a-9b30-8cd619de91d2%2F03e8d490-a102-4000-ab41-239a247607d4%2F4zdx2g8_processed.png&w=3840&q=75)
Transcribed Image Text:**Discrete-Time Signal Processing Quiz**
**Question:**
Select the correct expression for \( x[n] \) where:
\[ X(e^{j\omega}) =
\begin{cases}
4 & \text{for } 0 < \omega \leq \pi \\
0 & \text{Otherwise}
\end{cases}
\]
**Options:**
1. \( \dfrac{4}{j2\pi n} \left( e^{-j\pi n} - 1 \right) \)
2. \( \dfrac{4}{j2\pi n} \left( e^{j\pi n} + 1 \right) \)
3. \( \dfrac{4}{j2\pi n} \left( e^{j\pi n} - 1 \right) \)
4. \( \dfrac{4}{j2\pi n} \left( e^{+j \pi n} + 1 \right) \)
**Explanation of Options:**
Each option represents a different Fourier inverse transform expression, which is used to determine the time-domain sequence \(x[n]\) from the frequency-domain representation \(X(e^{j \omega})\). The correct expression must satisfy the given condition for \(X(e^{j \omega})\).
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