%Matlab code for Fourier Series
clear all
close all
%All time values
X=linspace(-1,1,1001);
%Loop for creating the function
for i=1:length(X)
if X(i)>=-1 && X(i)<0
zz(i)=0;
else
zz(i)=1-(X(i)).^2;
end
end
figure(1)
%Plotting the function
plot(X,zz)
xlabel('x')
ylabel('f(x)')
title('Plotting of Actual data')
a1=X(1); b1=X(end);
l=(b1-a1)/2;
%Fourier series of the function for finding a and b
coefficients
for j=1:200
ss1=zz.*cos(j*pi*X/l);
%all a values of the Fourier series
aa(j)=(1/l)*trapz(X,ss1);
ss2=zz.*sin(j*pi*X/l);
%all b values of the Fourier series
bb(j)=(1/l)*trapz(X,ss2);
end
%a0 value of Fourier series
aa0=(1/l)*trapz(X,zz);
X=linspace(-3,3,6001);
s=aa0/2;
%all an and bn terms
fprintf('Printing few terms for Fourier series\n')
for i=1:10
fprintf('\tThe value of a%d=%f and b%d=%f.
\n\n',i,aa(i),i,bb(i))
end
%Fourier series of the function
for i=1:200
s=s+bb(i)*sin(i*pi*X/l)+aa(i)*cos(i*pi*X/l);
if i==20
figure(2)
plot(X,s)
xlabel('time')
ylabel('f(t)')
title('Fourier series of
given function for 20 terms')
elseif i==200
figure(3)
plot(X,s)
xlabel('time')
ylabel('f(t)')
title('Fourier series of
given function for 200 terms')
end
end
%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%
Using MATLAB (a) Find the Fourier series for 25 { O if 1 r<O 1-2 if 0<H<1 f(x) defined on the interval -1<rs...
(a) Find the Fourier series for 25 { O if 1 r<O 1-2 if 0<H<1 f(x) defined on the interval -1<rs1. T-2 (b) Using MATLAB, plot the first 20 terms and the first 200 terms of the Fourier series in the interval -3< r<3, In order to do this, the r-interval should be divided into 6001 cqually spaced points by making use of the MATLAB command linspace. (a) Find the Fourier series for 25 { O if 1 r
(a) Find the Fourier series for 25 { O if 1 r<O 1-2 if 0<H<1 f(x) defined on the interval -1<rs1. T-2 (b) Using MATLAB, plot the first 20 terms and the first 200 terms of the Fourier series in the interval -3< r<3, In order to do this, the r-interval should be divided into 6001 cqually spaced points by making use of the MATLAB command linspace. (a) Find the Fourier series for 25 { O if 1 r
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