Consider a random binary pulse waveform as an alyzed in Example 7.6, but with half-cosine pulses given by p(t) = cos(2πt / 2T)II(t / T). Obtain and sketch the auto correlation function for the two cases considered in Example 7.6, namely,

(a) a_k = ± A for all k, where A is a constant, with R_m = A², m = 0, and R_m = 0 otherwise.

(b) a_k = A_k + A_{k_1}    with A_k = ± A and    E[A_kA_k+m] = A², m = 0, and zero otherwise.

(c) Find and sketch the power spectral density for each preceding case.