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(e jm - 1) 2m (e + 1) Pen (ein (ejm – 1) 스(etim + 1)

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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**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 \(X(e^{j \omega})\).
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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