1. [20 points]
A sketch of $X(\omega)$ is provided below. If $y(t) = \sin(5t)$, sketch the gain of the Fourier
Transform $H(\omega) = \mathcal{F}\{x(t)y(t)\}$. Then, if $H(\omega)$ represents a filter, answer the
following questions:
a) Is it lowpass or bandpass?
b) If a DC input of 10 Volts is applied, what is the magnitude of the output?
c) If the input is 10 Vac at 15 r/s, what is the magnitude of the output?