In natural sampling, an analog signal g (t) is multiplied by a periodic train of rectangular pulses c (t). Given that the pulse repetition frequency of this periodic train is ƒb and the duration of each rectangular pulse is T (with ƒb T << 1), do the following:

(a) Find the spectrum of the signal s (t) chat results from the use of natural sampling; you may assume that rime t = 0 corresponds to the midpoint of a rectangular pulse in c (t)

(b) Show that the original signal m (t) may be recovered exactly from its naturally sampled version, provided that the conditions embodied in the sampling theorem are satisfied.