Question

Problem 3: Let X(t) be a random process with autocorrelation function R_X(?) = 2?(?). The random process X(t) is input to an LTI system whose frequency response is given by: H(?) = 3 rect((? - 20?)/(4?)) + 3 rect((? + 20?)/(4?)). Let Y(t) be the output random process. 1. Find the average power of X(t) using its autocorrelation function. 2. Find the power spectral density (PSD) of X(t). 3. Find the average power of X(t) using its power spectral density (PSD). 4. Find the PSD of Y(t). 5. Find the average power of Y(t) using its PSD. 6. Find the autocorrelation function of Y(t). 7. Find the average power of Y(t) using its autocorrelation function.

          Problem 3:
Let X(t) be a random process with autocorrelation function R_X(?) = 2?(?). The random process X(t) is input to an LTI system whose frequency response is given by:
H(?) = 3 rect((? - 20?)/(4?)) + 3 rect((? + 20?)/(4?)).
Let Y(t) be the output random process.
1. Find the average power of X(t) using its autocorrelation function.
2. Find the power spectral density (PSD) of X(t).
3. Find the average power of X(t) using its power spectral density (PSD).
4. Find the PSD of Y(t).
5. Find the average power of Y(t) using its PSD.
6. Find the autocorrelation function of Y(t).
7. Find the average power of Y(t) using its autocorrelation function.

Problem 3:
Let X(t) be a random process with autocorrelation function RX(?) = 2?(?). The random process X(t) is input to an LTI system whose frequency response is given by:
H(?) = 3 rect((? - 20?)/(4?)) + 3 rect((? + 20?)/(4?)).
Let Y(t) be the output random process.
1. Find the average power of X(t) using its autocorrelation function.
2. Find the power spectral density (PSD) of X(t).
3. Find the average power of X(t) using its power spectral density (PSD).
4. Find the PSD of Y(t).
5. Find the average power of Y(t) using its PSD.
6. Find the autocorrelation function of Y(t).
7. Find the average power of Y(t) using its autocorrelation function.

Added by Laura B.

Question

Please give Ace some feedback