Lab No.09

Fourier Series (Sum of Sinusoids)

CECOS College of Engineering and IT March – July 2012

Designed by : Dawar Awandawar@cecos.edu.pk

CECOS College of Engineering and IT March – July 2012

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.

Concept

CECOS College of Engineering and IT March – July 2012

Example : Square wave

CECOS College of Engineering and IT March – July 2012

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

Adding first three harmonics

Example : Square wave

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

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

Sawtooth Wave

Fourier series approximation of sawtooth wave is given

by the following equation

CECOS College of Engineering and IT March – July 2012

CECOS College of Engineering and IT March – July 2012

Task

Plot the following expression for N=10

CECOS College of Engineering and IT March – July 2012

Triangular Wave

Fourier series approximation for a triangular wave is

given be the following equation.

Task

Plot the following equation for k=10

CECOS College of Engineering and IT March – July 2012