1.
Lab No.09
Fourier Series (Sum of Sinusoids)
Designed by : Dawar Awan
dawar@cecos.edu.pk
CECOS College of Engineering and IT
March – July 2012
2.
Concept
Fourier series theory states that a periodic wave can be
represented as a summation of sinusoidal waves with
different frequencies, amplitudes and phase values.
The frequencies of the sinusoids are harmonically
related.
fk = k.fo
Where fo is the fundamental frequency and fk is the kth
harmonic.
CECOS College of Engineering and IT
March – July 2012
3.
Example : Square wave
CECOS College of Engineering and IT
March – July 2012
4.
Example : Square wave
A square wave can be approximated by adding sine
waves, related to each other according to the following
equation.
Better approximation is achieved by increasing the
number of harmonics added
It can be seen that a square wave is composed of odd
harmonics
CECOS College of Engineering and IT
March – July 2012
5.
Example : Square wave
Adding first three harmonics
x=sin(2*pi*f*t);
y=(1/3).*sin(2*3*pi*f*t);
z=(1/5).*sin(2*5*pi*f*t);
w=4/pi*(x+y+z);
plot(t,w,)
CECOS College of Engineering and IT
March – July 2012
6.
Task
Approximate the square wave by adding first 10, 50, 100
harmonics. Observe the difference between the three
results.
CECOS College of Engineering and IT
March – July 2012
7.
Sawtooth Wave
Fourier series approximation of sawtooth wave is given
by the following equation
CECOS College of Engineering and IT
March – July 2012
8.
Task
Plot the following expression for N=10
CECOS College of Engineering and IT
March – July 2012
9.
Triangular Wave
Fourier series approximation for a triangular wave is
given be the following equation.
CECOS College of Engineering and IT
March – July 2012
10.
Task
Plot the following equation for k=10
CECOS College of Engineering and IT
March – July 2012
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