1. Consider a signal $f(t)$ whose Fourier Transform is $f (Womega)=\chi_{[-20,20]}(\omega)$. Let us modulate this signal with $\cos (2 \pi 30 t) $. a) Draw the modulated signal in frequency domain. b) What would you do to demodulate this signal? c) Let us sample $f(t) $ with a) $5 \mathrm{-Hz}$. b) $30 \mathrm{-Hz] $. In both cases, draw the sampled signal in frequency domain. In which case(s) we can recover the original signal from the sampled signal? Note: $\omega=2 \pi f$, where $f$ is frequency, measured in Hertz. CS.VS. 1126