Problem 1. Indicate whether each statement below is true or false. Justify your answers.
(a) Continuous time Fourier series cannot represent periodic signals while Fourier trans-
form can represent both periodic and aperiodic signals.
(b) For $T_0 > 0$, the impulse train $s(t) = \sum_{n=-\infty}^{\infty} \delta(t - nT_0)$ is equal to the summation of a
finite number of exponential terms.
Problem 2 - Fourier Transform.
(a) A system has a frequency response $H(\omega) = \frac{100}{j\omega + 200}$ and its impulse response is denoted
by $h(t)$. Assume that $h(t)$ is modulated as $h_1(t) = h(t)[sin(\omega_0t) + cos(\omega_1t)]$. What is the
frequency response $H_1(\omega)$?
(b) Assume that the output of a \"mixer\" device, $y(t)$, is the multiplication of two inputs
$x_1(t)$ and $x_2(t)$. Given that $x_1(t) = 10sinc(20t)$ and $x_2(t) = 5cos(500\pi t)$, calculate the
Fourier transform of $y(t) = x_1(t)x_2(t)$.
