Using the defining equations, compute the inverse Fourier transform of the following signals: (Part a) X₁ (jw) =j (8(w - wc) - 8(w + wc)) (Part b) X₂ (jw) = S(w - wc) + 8(w + wc)
Using the defining equations, compute the inverse Fourier transform of the following signals: (Part a) X₁ (jw) =j (8(w - wc) - 8(w + wc)) (Part b) X₂ (jw) = S(w - wc) + 8(w + wc)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![**Title: Inverse Fourier Transform of Given Signals**
**Problem Statement:**
Using the defining equations, compute the inverse Fourier transform of the following signals:
**(Part a)**
\[ X_1(j\omega) = j \left( \delta(\omega - \omega_c) - \delta(\omega + \omega_c) \right) \]
**(Part b)**
\[ X_2(j\omega) = \delta(\omega - \omega_c) + \delta(\omega + \omega_c) \]
**Instructions:**
Sketch the time-domain signal that you obtained in each part. Do recall that if the signal is complex-valued, you can plot its real/imaginary component OR its magnitude/phase.
You can assume that \(\omega_c\) is a real-valued, positive scalar.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F039207b8-632a-4dc4-a3c4-fd77b3c684b4%2Fa73137ef-0acb-48d5-b0e8-7d8dfd424173%2Fx7m60kc_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Inverse Fourier Transform of Given Signals**
**Problem Statement:**
Using the defining equations, compute the inverse Fourier transform of the following signals:
**(Part a)**
\[ X_1(j\omega) = j \left( \delta(\omega - \omega_c) - \delta(\omega + \omega_c) \right) \]
**(Part b)**
\[ X_2(j\omega) = \delta(\omega - \omega_c) + \delta(\omega + \omega_c) \]
**Instructions:**
Sketch the time-domain signal that you obtained in each part. Do recall that if the signal is complex-valued, you can plot its real/imaginary component OR its magnitude/phase.
You can assume that \(\omega_c\) is a real-valued, positive scalar.
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