VIPSolutions**Final Answers:** 1. The average power of $X(t)$ is $P_X = \infty$. 2. The PSD of $X(t)$ is $S_X(\omega) = 2$. 3. The average power of $X(t)$ from its PSD is $P_X = \infty$. 4. The PSD of $Y(t)$ is $$ S_Y(\omega) = 18\text{rect}\left(\frac{\omega - 20\pi}{4\pi}\right) + 18\text{rect}\left(\frac{\omega + 20\pi}{4\pi}\right) $$ 5. The average power of $Y(t)$ from its PSD is $P_Y = 72$. 6. The autocorrelation of $Y(t)$ is $$ R_Y(\tau) = \frac{36\cos(20\pi\tau)\sin(2\pi\tau)}{\pi\tau} $$ 7. The average power of $Y(t)$ from its autocorrelation is $P_Y = 72$. rewrite as it is
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**Final Answers:** 1. The average power of $X(t)$ is $P_X = \infty$. 2. The PSD of $X(t)$ is $S_X(\omega) = 2$. 3. The average power of $X(t)$ from its PSD is $P_X = \infty$. 4. The PSD of $Y(t)$ is $$ S_Y(\omega) = 18\text{rect}\left(\frac{\omega - 20\pi}{4\pi}\right) + 18\text{rect}\left(\frac{\omega + 20\pi}{4\pi}\right) $$ 5. The average power of $Y(t)$ from its PSD is $P_Y = 72$. 6. The autocorrelation of $Y(t)$ is $$ R_Y(\tau) = \frac{36\cos(20\pi\tau)\sin(2\pi\tau)}{\pi\tau} $$ 7. The average power of $Y(t)$ from its autocorrelation is $P_Y = 72$. rewrite as it is
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Asked by: Umesh
Created at: 2025-08-02 00:56:55
Asked by: Umesh
Created at: 2025-08-02 00:56:55
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**Final Answers:**
1. The average power of \( X(t) \) is \( P_X = \infty \).
2. The PSD of \( X(t) \) is \( S_X(\omega) = 2 \).
3. The average power of \( X(t) \) from its PSD is \( P_X = \infty \).
4. The PSD of \( Y(t) \) is
$$
S_Y(\omega) = 18\text{rect}\left(\frac{\omega - 20\pi}{4\pi}\right) + 18\text{rect}\left(\frac{\omega + 20\pi}{4\pi}\right)
$$
5. The average power of \( Y(t) \) from its PSD is \( P_Y = 72 \).
6. The autocorrelation of \( Y(t) \) is
$$
R_Y(\tau) = \frac{36\cos(20\pi\tau)\sin(2\pi\tau)}{\pi\tau}
$$
7. The average power of \( Y(t) \) from its autocorrelation is \( P_Y = 72 \).
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