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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)

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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.
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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