Problem 1 (10 points)
For the signal shown below,
(a) (6 points) Using the general form of Fourier coefficients given as
\[
X_{n}=\frac{1}{T_{0}} \int_{-T_{0} / 2}^{T_{0} / 2} x(t) e^{-j 2 \pi\left(n f_{0}\right) t} d t
\]
derive the expression for the Fourier coefficients of the signal. Specify the DC value, and show the expressions for the magnitude and phase.
(b) (4 points) Using the expression for the Fourier coefficients, synthesize the periodic signal as a linear combination of sinusoids.
