Consider the raised cosine pulse x(t) = [1 + cos( t)] (u(t + 1) u(t 1)) (a) Carefully plot x(t). (b) Find the

Consider the raised cosine pulse

x(t) = [1 + cos(π t)] (u(t + 1) − u(t − 1))

(a) Carefully plot x(t).

(b) Find the Fourier transform of the pulse

p(t) = u(t + 1) − u(t − 1)

(c) Use the definition of the pulse p(t) and the modulation property to find the Fourier transform of x(t) in terms of P(Ω) = F[p (t)].