Midterm 2 ECE 301
NAME:
ID
Instructions:
1) There are 4 questions. Try to answer all questions.
2) Do not open the booklet unless instructed to do so.
3) Write legibly and show all your steps.
4) Do not copy or cheat.
5) No notes, formula sheets or calculators are allowed in this exam.

1.
Find the Fourier Series for the signal x[n],
with period N=9:
(No need to
plot the spectrum, just finding the Fourier coefficients is enough)
𝑥𝑥
[
𝑛𝑛
] = 1 + sin
�
2
𝜋𝜋
𝑁𝑁
𝑛𝑛�
+ 5 cos
�
2
𝜋𝜋
𝑁𝑁
𝑛𝑛� −
2 cos(
4
𝜋𝜋
𝑁𝑁
𝑛𝑛
)

2.
Find the Fourier series for the following discrete-time periodic signal x[n],
with
𝑁𝑁
1
= 4
and the period
𝑁𝑁
= 10.
(No need to plot the spectrum, just
finding the Fourier coefficients is enough)

3.
(a)
Find the Fourier Transform for the following signal

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- Fourier Series