Consider a binary communication system. The rectangular pulse p(t) and the triangular pulse q(t) are defined...

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Consider a binary communication system. The rectangular pulse p(t) and the triangular pulse q(t) are defined by (1, 0<t<T, p(t) = l0, else, and 1 %3D 0 st<T, T' (0, To send "I", p(t) is transmitted. To send "0", -q(t) is transmitted. The channel is contaminated by AWGN with power spectral density of No/2. The following receiver is q(t) = else. used for detection. T h(t) >y or < y The impulse response of the LTI filter h(t) is given by (1, 0st< 2T/3, else. h(t) = {0, a. Suppose that "]" is sent. Determine the probability of error in terms of T, y, No- b. Determine the minimax threshold. c. Suppose that you can change the LTI filter and the threshold at the receiver. i. Sketch the impulse response of the optimal filter. ii. Determine the probability of error with the optimal filter and the associated optimal threshold. Consider a binary communication system. The rectangular pulse p(t) and the triangular pulse q(t) are defined by (1, 0<t<T, p(t) = l0, else, and 1 %3D 0 st<T, T' (0, To send "I", p(t) is transmitted. To send "0", -q(t) is transmitted. The channel is contaminated by AWGN with power spectral density of No/2. The following receiver is q(t) = else. used for detection. T h(t) >y or < y The impulse response of the LTI filter h(t) is given by (1, 0st< 2T/3, else. h(t) = {0, a. Suppose that "]" is sent. Determine the probability of error in terms of T, y, No- b. Determine the minimax threshold. c. Suppose that you can change the LTI filter and the threshold at the receiver. i. Sketch the impulse response of the optimal filter. ii. Determine the probability of error with the optimal filter and the associated optimal threshold.