Response to the following problem:
The Nyquist criterion gives the necessary and sufficient condition for the spectrum X( f ) of the pulse x(t) that yields zero ISI. Prove that for any pulse that is band-limited to | f | < 1/T , the zero-ISI condition is satisfied if Re[X( f ), for f > 0, consists of a rectangular function plus an arbitrary odd function around f = 1/2T , and Im[X( f )] is any arbitrary even function around f = 1/2T .