View source for Fourier Series Example Script

===Sampled Fourier Series===
This is a script that plots a few terms of the Fourier series of a square wave and then plots some samples of it in red *'s.  You can copy this and paste it into your editor and run it from octave or just paste it into an octave window to see the plot.

 % This script plots a Fourier Series for a Square Wave
 clf;
 t=0:.01:10;
 T=2.5
 M=50    
 sum1=0;
 for m=1:2:M,
     sum1 = sum1+4/m/pi*sin(m*pi/2)*cos(2*pi*m*t/T);
 end
 plot(t,sum1,'b-',t(1:10:end),sum1(1:10:end),'r*')
 title('Fourier Series Representation of a Square Wave')
 xlabel('time (seconds)')
 ylabel('Function')
 grid on;
 axis([0,10,-2,2])
 legend('Five Terms','Five Terms Sampled')
 print("squarewave.png","-dpng")  % Prints the plot to a png file called squarewave.png

===Fourier Series Solution for Sinusoidal Steady State Response of a Low Pass Filter===
This goes with the [http://people.wallawalla.edu/~Rob.Frohne/ClassNotes/ENGR351/2010f/Background/index.php class notes for October 1, 2010.] 

[[File:LowPassFilter.png]]

 clf;
 t=0:.01:10;
 T=pi;
 R=2;
 C=1;
 M=101;
 vin=0;
 current =0;
 for n=1:2:M,
 	vin = vin+1./(n.*pi).*(3.*sin(pi.*n./2)-sin(3.*n.*pi./2)).*cos(2.*pi.*n.*t./T);
 	current = current+1./(sqrt(R.^2+1./((2.*pi.*n./T).^2*C.^2))).*1./(n.*pi).*(3.*sin(pi.*n./2)-sin(3.*n.*pi./2)).*cos(2.*pi.*n.*t. /T-atan2(-1,2*pi*n/T*R*C));
 end
 vout=vin-R.*current;
 plot(t,vin,'b-',t,vout)
 title('Fourier Series Representation of a Square Wave')
 xlabel('time (seconds)')
 ylabel('Function')
 grid on;
 axis([0,10,-2,2])
 legend('Input Voltage','Output Voltage')
 print("LowPass.png","-dpng")  % Prints the plot to a png file called squarewave.png

The output produces a nice plot.
[[File:LowPass.png|600pix]]