Answer Happy

Consider a periodic square wave with a fundamental period of
𝑇=4. Over the interval −2<
𝑡 <2, the square wave is described by:
𝑥5(𝑡)={3, |𝑡|≤0.5
0, |𝑡|>0.5
a) [2 pts] what do you expect the Fourier
series coefficients to be?

b) [3 pts] Create a symbolic expression for 𝑥5(𝑡) and then input
that to the int function to
create a symbolic expression for the Fourier series
coefficients.
(Note: You will need to define two symbolic variables for
this.)

c) [5 pts] Use the subs function and your expression from part b)
to determine the Fourier
series coefficients for −100≤𝑘 ≤100. Plot the resulting Fourier
series coefficients
from -20 to 20 using the stem function. (xlim may be useful
here)
(Note: You will need to calculate the 𝑘 =0 term separately to avoid
a division by zero
error for this particular function.)

d) [5 pts] Create symbolic expressions of 𝑥𝑁(𝑡) for 𝑁=1,3,9,𝑎𝑛𝑑
100, and use fplot
to plot each of the functions on the same plot with 𝑥5(𝑡) for
−2≤𝑡≤2.
(Hint: The symsum function can be helpful here. Also, the hold
function will be needed
to put all the plots on the same figure.)

e) [1 pts] What are the values of 𝑥𝑁(𝑡) for 𝑁 =1,3,9,𝑎𝑛𝑑 100 at 𝑡
=±0.5? Does this
make sense?