ECE 301 Project 2: Fourier Series
Due June 29, 2011
Introduction
This project is intended to familiarize you with fourier series beyond homework assignments. All materials necessary for
the project are available on the website (dea.ecn.purdue.edu/ece301).
Please familiarize yourself with the analysis and
synthesis equations for the ContinuousTime Fourier Series (CTFS) before starting the project.
1
Square Wave
Download square
wave.mat and load it in Matlab (
load square
wave.mat
). It will contain a vector continaing the time,
t
, a vector with the square waveform,
x
, and a variable with the period,
T
.
1.1
Fourier Series Coefficients
Find the formula for the Fourier Series (CTFS) Coefficients,
a
k
. Next, find an expression for
b
k
such that:
x
(
t
) =
b
0
+
∞
X
k
=1
b
k
cos
2
π
T
kt
(1)
Let ˜
x
(
t
) be an approximation to
x
(
t
) that has only the first few harmonics.
˜
x
(
t
) =
b
0
+
N
X
k
=1
b
k
cos
2
π
T
kt
(2)
1.2
Deliverables
For the first 8 harmonics (not including
b
0
and therefore there are 6 total graphs), plot
x
(
t
) and ˜
x
(
t
) in the same figure
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 Fall '06
 V."Ragu"Balakrishnan
 Fourier Series, Square wave, UCI race classifications, Tour de Georgia, Waveform

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