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clear;
close;
a = 1;
p = 1;
frequency = 50;//1/(2*%pi);  
period = 1/frequency;    
x = [(-period/2+p):0.0001:(period/2+p)];  
f = zeros(length(x)); 
for i = 1:length(x)     
   if (-period/2+p) <= x(i) & x(i) < p then         
       f(i) = -a;            
   else         
       f(i) = a;       
   end 
end  
plot2d(x,f,5);  

t = [(-period/2+p):0.0001:(period/2+p)];  
w = 2*%pi/period; 
fn = zeros(1,length(t)); 
n = 50;  
for k=1:n     
      fn = fn + 1/k*( -2*sin(k*p) - sin(k*%pi-k*p) + sin(k*%pi+k*p) ) * cos(k*w*t) ...             
                 + 1/k*( 2*cos(k*p) - cos(k*%pi-k*p) - cos(k*%pi+k*p) ) * sin(k*w*t); 
end 
fn = a/%pi * fn;   
plot2d(t,fn,2);  

xlabel('t') 
ylabel('y(t)') 
legend('exact curve', 'fourier series')

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x = [(-period/2+p):0.0001:(period/2+p)];  
f = zeros(length(x)); 
for i = 1:length(x)     
   if (-period/2+p) <= x(i) & x(i) < p then         
       f(i) = -a;            
   else         
       f(i) = a;       
   end 
end