# how to plot fourier series in matlab

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omar alblooshi on 16 Mar 2018
Commented: Rik on 7 Mar 2022
how to plot fourier series in matlab
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/

Abraham Boayue on 18 Mar 2018
Edited: Abraham Boayue on 15 Jun 2018
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
##### 1 CommentShowHide None
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/

Abraham Boayue on 18 Mar 2018
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.
##### 1 CommentShowHide None
Rik on 7 Mar 2022
Comment posted as flag by @Muhammet Bilgiç:
this guy is great

Abhishek Ballaney on 16 Mar 2018
https://in.mathworks.com/help/curvefit/fourier.html
##### 2 CommentsShowHide 1 older comment
vikrant rana on 26 Jan 2022
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.

Mohamed Abugammar on 10 Apr 2019
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
##### 1 CommentShowHide None
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/

Dhiya Eid on 20 Jul 2020
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

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/
Gülcan söm on 30 Dec 2020
how to write if i want to solve f(x)=cos(3x) and find the fourier series of f(x)