Consider the following three continuous-time signals with a fundamental period of T =

Chapter 3, Problem 3.25

(choose chapter or problem)

Consider the following three continuous-time signals with a fundamental period of T = 1/2:

\(\begin{aligned}
x(t) & =\cos (4 \pi t), \\
y(t) & =\sin (4 \pi t), \\
z(t) & =x(t) y(t) .
\end{aligned}\)

(a) Determine the Fourier series coefficients of x(t).

(b) Determine the Fourier series coefficients of y(t).

(c) Use the results of parts (a) and (b), along with the multiplication property of the continuous-time Fourier series, to determine the Fourier series coefficients of z(t) = x(t)y(t).

(d) Determine the Fourier series coefficients of z(t) through direct expansion of z(t) in trigonometric form, and compare your result with that of part (c).