fourier transform shifted graphic

clear all; close all; clc;
 
x1=-37:0.1:-31.5;
eq1 = 0*x1+3.3; 
 
x2=-31.5:0.1:-29.5;
eq2 = 3.3*(-29.5-x2)/(2); 

x3=-29.5:0.1:-24;
eq3 = 3.3*(-29.5-x3)/(5.5);  

x4=-24:0.1:-18.5;
eq4=0*x4-3.3;

x5=-18.5;
eq5 =3.3;

x6=-18.5:0.1:-13;
eq6 = 0*x6+3.3; 

x7=-13:0.1:-11;
eq7 = 3.3*(-11-x7)/(2);  

x8=-11:0.1:-5.5;
eq8 = 3.3*(-11-x8)/(5.5);  
 
x9=-5.5:0.1:0;
eq9 = 0*x9-3.3; 

x10=0;
eq10=3.3;

x11=0:0.1:5.5;
eq11 = (0*x11)+3.3; 

x12=5.5:0.1:7.5;
eq12 = 3.3*(7.5-x12)/2;  

x13=7.5:0.1:13;
eq13=3.3*(7.5-x13)/5.5;  

x14=13:0.1:18.5;
eq14=(0*x14)-3.3; 

x15=18.5;
eq15 = 3.3;


x = [x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 ];
y = [eq1 eq2 eq3 eq4 eq5 eq6 eq7 eq8 eq9 eq10 eq11 eq12 eq13 eq14 eq15 ];
 
plot(x, y, 'r')
grid on; hold on;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

syms t  
A=3.3;
t1=(5+6)/2;               
t2=t1+2;                   
t3=t1+t2;                  
t4=t1+t3;                 
w=(2*pi)/t4;
sum=0;  


a0=(2/t4)*(int(t*0+A,0,t1)+int(A*(7.5-t)/(2),t1,t2)+int(A*(7.5-t)/(5.5),t2,t3)+int(t*0-A,t3,t4))
for n=1:20 
  
    an=(2/t4)*(int((t*0+A)*cos((n*w)*t),0,t1)+int(A*(7.5-t)/(2)*cos((n*w)*t),t1,t2)+int(A*(7.5-t)/(5.5)*cos((n*w)*t),t2,t3)+int((t*0-A)*cos((n*w)*t),t3,t4))  
    bn=(2/t4)*(int((t*0+A)*sin((n*w)*t),0,t1)+int(A*(7.5-t)/(2)*sin((n*w)*t),t1,t2)+int(A*(7.5-t)/(5.5)*sin((n*w)*t),t2,t3)+int((t*0-A)*sin((n*w)*t),t3,t4))  
    sum=sum+((an*cos((n*w)*t)+bn*sin((n*w)*t)+(a0/2)))
    
end 
grid on;hold on;  
ezplot(t,(sum),[-2*t4,t4]); 

I haven't been able to find out for hours why this graph is shifted. Maybe someone can help and see the error? Thanks.

Answer 1

[David Goodmanson]

Hello MK

First of all it is not a good idea to have a variable called 'sum' because that's the name of a basic Matlab function. Matlab is case sensitive so when I ran the code I changed the variable to 'Sum' (easy because when you change the name of a variable in the editor, Matlab offers up an optional autochange of every other instance of the variable).

The problem happens because you have a0/2 inside the for loop, so that a0/2 gets added in 20 times. If you remove a0/2 from the loop and add Sum = Sum + a0/2 past the end of the loop, it works.

[yok]

thanks a lot, how do i miss this.

[David Goodmanson]

Hi yok,

We have all been there, staring at the same set of expressions for hours and hours, having some sort of mental block. Then someone else comes along and says, what about <whatever> and then we say, aak! how could I have been such an idiot? It happens. One of the useful things about this site is having several sets of eyes take a look..