Assignment:
1. The continuous time Gaussian process x has zero mean and autocorrelation
rx(t,τ ) = e-ƒ0|τ| |cos 2Πƒ0t|
a) Find P [x(T1) > 1] and P [x(T1) > x(2T1)], with T1 = 1/(8f0).
b) Write the expression of the average PSD of x.
2. Let s(t) be a Gaussian random process with zero mean and PSD
Ps(ƒ) = 10-2/2B rect (ƒ/2B) B = 106 Hz
The process is filtered by a filter with frequency response
Çch(ƒ) = Ç0 rect (ƒ/2Bch)
With Compute Ç0 = 0.3, Bch = 109 Hz. the probability that the amplitude of the signal at the filter output, y(t), lies in the range [-0.6, 0.6].