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

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

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