A real-valued signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$  is passed through a linear time invariant system whose frequency response is $$H\left( f \right) = \left\{ {\matrix{ {{e^{ - j4\pi f,}}} & {\left| f \right| \le {W \over 2}} \cr {0,} & {\left| f \right| > {W \over 2}} \cr } } \right.$$
The output of the system is