Question

Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is Y(t) White Noise? Explain. 4. Is Y(t) Wide-Sense Stationary Randon Proccss (WSSRP)? Explain 5. Is Y(t) Gaussian Random Process? If yes what are the inean and the variance of this process? 6. What is the probability density function of the random variable Y (t) at any time instant t?. 7. What is the probability that the output Y(t1) lics in the range [-0.1, 0.1? Assune No/T 2. 8. Now assume that the input, s(t), is a signal shown in Figure 2. Plot the output signal, y(t). Find the values of the output at T, 2T and 3T. 9. Now assume that the input are both signals s(t) and X(t), Find the total output sampled at T 10. Find the probability that the total output sampled at T is less than zero. Suct)FTEf] s(t) 3T 21 T Time (sec) Figure 2: Input signal s(t).

Answer 1

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