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• 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