how to plot fourier series in matlab

 how to plot fourier series in matlab

[Abraham Boayue]

Have you done the integrals to fined the a0, an and bn? If so, what is the expression you got for the fourier series?

[Akira Agata]

Regarding the question (1) in the picture, I would recommend try to calculate by hand first, for your better understanding of Fourier transformation of periodic function.

[Korosh Agha Mohammad Ghasemi]

clear all;clc; 
syms x  n pi
% pi=3.14; 
sum=0;  
y=x   %function you want 
a0=(1/pi)*int(y,x,-pi,pi) 
% for n=1:5 
        %finding the coefficients 
    an=(1/pi)*int(y*cos(n*x),x,-pi,pi) 
    bn=(1/pi)*int(y*sin(n*x),x,-pi,pi)    
    sum=a0/2+(an*cos(n*x)+bn*sin(n*x)) 
% end 
ezplot(x,y,[-pi,pi])
grid on;hold on;  
ezplot(x,(sum+a0/2),[-pi,pi])
% https://www.instagram.com/koroshkorosh1/
syms x pi
F =(1/pi) * int(x^2+5*x,'Hold',true)
bn=(1/pi)*int(y*sin(n*x),x,-pi,pi), G = bn
Gcalc = release(G)
Fcalc = int(bn)
clear all;clc; 
syms x  pi n
% pi=3.14; 
sum=0;  
y= x + (x^2) ;   %function you want 
a0=(1/pi)*int(y,x,-pi,pi)  
% for n=1:3 
        %finding the coefficients 
    an=(1/pi)*int(y*cos(n*x),x,-pi,pi)  
    bn=(1/pi)*int(y*sin(n*x),x,-pi,pi)     
    sum=sum+(an*cos(n*x)+bn*sin(n*x))   
% end 
% https://www.instagram.com/koroshkorosh1/
ezplot(x,y,[-3.14,3.14]); 
grid on;hold on;  

ezplot(x,(sum+a0/2),[-3.14,3.14]) 
% https://www.instagram.com/koroshkorosh1/

[Salihath]

how to write matlab code for time modulated array

[Rik]

@Salihath Since your post was not an answer, I moved it to the comment section. Have a read here and here. It will greatly improve your chances of getting an answer.

Answer 1

[Abraham Boayue]

Here is what your Fourirer series would like if my calculations were made correctly. An attachment of the solution is also included for your reference. Take care for now.

clear variables
close all
% Fourier series of neither even nor odd function
% Decompose f(x) into even (fe) and odd (fo) functions.
% fe = (f(x) + f(-x))/2, fo = (f(x) - f(-x))/2
N = 500;
L = 4;
xd = -L:2*L/(N-1):L;
y1 = -1/8*xd.^2;
y2 = 1/8*xd.^2;
fo = y1.*(-L<=xd & xd<=0) +y2.*(0<=xd & xd<=L);
fe = 4-xd.^2/8;
f2 = fe + fo;
a0 = 10/3;
% Generate the fourier series of f(x)
y = zeros(1,N);
x = [];
K = 80;
for k = 1:K
 ck = 1/(pi*k);
 an  = (2*L*(-1).^(k+1))*ck^2;
 bn = L*(-1).^(k+1)*ck  + (2*L*ck^3)*((-1)^k-1);
 y = y + (an*cos(pi*k/L*xd)+ bn*sin(pi*k/L*xd));   % For fe and fo
 x = [x;y];
end
y = a0 +y;
x = a0 +x;

% Color codes
s = distinguishable_colors(K); % search this function on mathworks

figure
subplot(121) % Plot f(t)
plot(xd,f2,'linewidth',2.5,'color',s(1,:))
line(xlim,[0 0],'color',s(6,:),'linewidth',3);
line([0 0],ylim,'color',s(6,:)','linewidth',3);
ylim([-.5 4]);
a= xlabel('\itt\rm (seconds)');
set(a,'fontsize',20);
a = ylabel('\itf\rm(\itt\rm)');
set(a,'fontsize',20);
a= title('f(t)');
set(a,'fontsize',14);
grid

subplot(122) % Plot fouries series of f(t);
hold on
q = length(x(:,1));
M = 1:q;
for i = 1:6:q
plot(xd,x(i,:),'linewidth',2.5,'color',s(i,:),'DisplayName',sprintf('S = %1.2f',M(i)))
end
a= title('Fourier series of f(t)');
set(a,'fontsize',14);
a= xlabel('\itt\rm (seconds)');
set(a,'fontsize',20);
a = ylabel('\itf\rm(\itt\rm)');
set(a,'fontsize',20);
line(xlim,[0 0],'color',s(6,:),'linewidth',3);
line([0 0],ylim,'color',s(6,:)','linewidth',3);
legend('-DynamicLegend','location','bestoutside');
grid

[Korosh Agha Mohammad Ghasemi]

clear all;clc; 
syms x  
pi=3.14; 
sum=0;  
y=exp(x);   %function you want 
a0=(1/pi)*int(y,x,-pi,pi); 
for n=1:3 
        %finding the coefficients 
    an=(1/pi)*int(y*cos(n*x),x,-pi,pi); 
    bn=(1/pi)*int(y*sin(n*x),x,-pi,pi);    
    sum=sum+(an*cos(n*x)+bn*sin(n*x));  
end 
% https://www.instagram.com/koroshkorosh1/
ezplot(x,y,[-pi,pi]); 
grid on;hold on;  
ezplot(x,(sum+a0/2),[-pi,pi]); 
% https://www.instagram.com/koroshkorosh1/

Answer 2

[Abraham Boayue]

The is the solution file, the math is a bit messy, but I assume that you are familiar with the material that you are studying.

[Rik]

Comment posted as flag by @Muhammet Bilgiç:

this guy is great

Answer 3

[Abhishek Ballaney]

https://in.mathworks.com/help/curvefit/fourier.html

[Korosh Agha Mohammad Ghasemi]

clear all;clc; 
syms x  
pi=3.14; 
sum=0;  
y=exp(x);   %function you want 
a0=(1/pi)*int(y,x,-pi,pi); 
for n=1:3 
        %finding the coefficients 
    an=(1/pi)*int(y*cos(n*x),x,-pi,pi); 
    bn=(1/pi)*int(y*sin(n*x),x,-pi,pi);    
    sum=sum+(an*cos(n*x)+bn*sin(n*x));  
end 
% https://www.instagram.com/koroshkorosh1/
ezplot(x,y,[-pi,pi]); 
grid on;hold on;  
ezplot(x,(sum+a0/2),[-pi,pi]); 
% https://www.instagram.com/koroshkorosh1/

[vikrant rana]

hey abhishek,

what would be the changes in code if y=(pi-x)/2

and the limits are from 0 to 2 pi

like i am trying to make changes in the code by substituiting my values i not happening.

i shall be thankful to you if you resolve my doubt.

Answer 4

[Mohamed Abugammar]

clc;

close all;

clear all;

dx=0.001;

L=pi;

x=(-1+dx:dx:1)*L;

n=length(x); nquart=floor(n/4);

% define the hat function;

f=0*x;

f(nquart:2*nquart)=4*(1:nquart+1)/n;

f(2*nquart+1:3*nquart)=1-4*[1:500]/n;

plot(x, f,'r','LineWidth', 2); hold on;

%% define the coffeciet

A0=sum(f.*ones(size(x)))*dx;

fFS = A0/2;

for k=1:10

Ak=sum(f.*cos(pi*k*x/L))*dx;

Bk=sum(f.*sin(pi*k*x/L))*dx;

fFS=fFS+Ak*cos(pi*k*x/L)+Bk*sin(pi*k*x/L);

plot(x,fFS);

pause(1); drawnow;

end

[Korosh Agha Mohammad Ghasemi]

clear all;clc; 
syms x  
pi=3.14; 
sum=0;  
y=exp(x);   %function you want 
a0=(1/pi)*int(y,x,-pi,pi); 
for n=1:3 
        %finding the coefficients 
    an=(1/pi)*int(y*cos(n*x),x,-pi,pi); 
    bn=(1/pi)*int(y*sin(n*x),x,-pi,pi);    
    sum=sum+(an*cos(n*x)+bn*sin(n*x));  
end 
% https://www.instagram.com/koroshkorosh1/
ezplot(x,y,[-pi,pi]); 
grid on;hold on;  
ezplot(x,(sum+a0/2),[-pi,pi]); 
% https://www.instagram.com/koroshkorosh1/

Answer 5

[Dhiya Eid]

Let f(x) be a 2π-periodic function such that f(x)=x2 for x∈[−π,π]. Find the Fourier series for the parabolic wave.

solve it in matlab

[Deniz Sezen]

Could you solve that question?

[Rik]

This is an 'answer' from almost 3 years ago. I doubt you will get a response.

Answer 6

[Korosh Agha Mohammad Ghasemi]

f=@(x)x.*(x>0 & x<-pi)-2*(x/pi+1).*(x>=-pi & x<=-pi/2);
n=50;
k=0:n;
a=1/pi*(integral(@(x)f(x).*cos(k*x),-pi,-pi/2,'ArrayValued',true)+integral(@(x)f(x).*cos(k*x),0,pi/2,'ArrayValued',true));
k=1:n;
b=1/pi*(integral(@(x)f(x).*sin(k*x),-pi,-pi/2,'ArrayValued',true)+integral(@(x)f(x).*sin(k*x),0,pi/2,'ArrayValued',true));
ffun=@(x)a(1)/2+sum(a(2:n+1).*cos((1:n)*x)+b(1:n).*sin((1:n)*x));
x=linspace(0,pi,200);
fx=arrayfun(@(x)ffun(x),x);
plot(x,fx,x,f(x))

% https://www.instagram.com/koroshkorosh1/

[Korosh Agha Mohammad Ghasemi]

clear all;clc; 
syms x  
pi=3.14; 
sum=0;  
y=exp(x);   %function you want 
a0=(1/pi)*int(y,x,-pi,pi); 
for n=1:3 
        %finding the coefficients 
    an=(1/pi)*int(y*cos(n*x),x,-pi,pi); 
    bn=(1/pi)*int(y*sin(n*x),x,-pi,pi);    
    sum=sum+(an*cos(n*x)+bn*sin(n*x));  
end 
% https://www.instagram.com/koroshkorosh1/
ezplot(x,y,[-pi,pi]); 
grid on;hold on;  
ezplot(x,(sum+a0/2),[-pi,pi]); 
% https://www.instagram.com/koroshkorosh1/

[taha bandrawala]

how to write if i want to solve f(x)=x^3 and find the fourier series of f(x)

[Gülcan söm]

how to write if i want to solve f(x)=cos(3x) and find the fourier series of f(x)