10.(10%) Find the interval of convergence of the series

(a)  (4%) Considering y1(t), y2(t), y3(t), and y4(t), the random processes that are wide-sense stationary are____________

(b) (3%) Considering y1(t), y2(t), y3(t), and y4(t), the random processes that are white are_______________

(c) (2%)Itis _____________(true/false) that the random processes y2(t) and y3(r) are statistically independent.

(d) (6%) The probability that z(t) is greater than 3 at t=20 is____________

(a) (4%) Compute a set of orthonormal basis functionsusing the Gram-Schmidt procedure, whereis proportional to sA(r). The signals sA(X), sB(t), sc(t), and sD(t) can be expressed as a linear combination of these basis functions as__________________________________________________________________________________________________________________ where the basis functions are________________________________________________________________________________________________________________________________________________________

(b) (4%) The TWO candidate signals that would result in minimum average transmitted energy, given that the two messages are equiprobable, are_______________.

(c) (4%) The TWO candidate signals that would provide the lowest average probability of a bit error are____________________________

(d) (6%) To increase data rate, suppose now you want to send THREE messages instead of two, which again occur with equal a priori probability. Suppose SA(t), SB(t), and sc(t) are chosen to represent these messages, and the power spectral density of the noise is . The union bound of the average symbol error probability is_____________________

(a) (3%) Let t0 = 3 and T=4, i.e. h(t) = s(4- t). Determine the mean and variance of the filtered and sampled noise term W.

(b) (6%) Again, let t0 = 3 and T=4. Please find the corresponding bit error rate (BER) of the ML receiver. (Express your answer in Q-function.)

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