Problem 3.16 Let p(t) = I{-¼, ½](t) denote a rectangular pulse of unit duration. Construct the signal ∞ m(t) = (-1)p(t — n) n=-∞ The signal m(t) is input to an FM modulator, whose output is given by where u(t) = 20 cos(2π fct +ø(t)) and a is chosen such that (0) = 0. (a) Carefully sketch both m(t) and (t) = 20π m(T)dT + a -∞ (t) as a function of time. (b) Approximating the bandwidth of m(t) as W ≈2, estimate the bandwidth of u(t) using Carson's formula. (c) Suppose that a very narrow ideal BPF (with bandwidth less than 0.1) is placed at fc + a. For which (if any) of the following choices of a will you get nonzero power at the output of the BPF: (i) a = .5, (ii) α = .75, (iii) a = 1.