Consider the periodic continuous-time signal
x(t) = 4 - (t - 2n)$^2$ for $2n \le t < 2(n + 1)$
for all integers $n$.
(a) Determine the continuous-time Fourier series (CTFS) coefficients
for $x(t)$.
(b) Use MATLAB to plot the real and imaginary parts and the mag-
nitude and phase of the CTFS coefficients for harmonic numbers
k = -20, -19, \dots, 20. Include your MATLAB code as part of
your solution.
(c) Use MATLAB to form the partial sums $x_N(t)$ of the CTFS and
plot the partial sums with the signal $x(t)$ for N = 1, 2, 5, 10, 50
and for $0 \le t < 2$. Include your MATLAB code as part of your
solution.
(d) Use MATLAB to plot the MSE of the partial sums you calculated
previously as a function of N for N = 1, 2, \dots, 50.
