1. Prove that a signal cannot be simultaneously timelimited and bandlimited.
2. The signal x(t) = sin(0.7πt) cos(0.5πt) is sampled using Fs = 1 Hz to yield a discretetime signal x[n]. Next, x[n] is filtered using an ideal high-pass digital filter that eliminates all frequencies below 3/10 Fs, the output of which is called y[n]. Finally, y[n] is passed through a perfect reconstruction filter at the rate Fs = 1 2 Hz. Find a simplified expression for y(t), the output of the reconstructor. Can this system operate in "real time"?