Question

1 point) Consider the Fourier series: nTTc a. Find the Fourier coefficients for the function f(x) 1.2 an b. Use the computer to draw the Fourier series of f(a), for x E[-18, 18], showing clearly all points of convergence. Also, show the graphs with the partial sums of the Fourier series using n5 and n20 terms. What do you observe?

Answer 1

万n ano 4 пт n 0.4X36 Co

%Matlab code for Fourier Series clear all close all %All time values X-linspace (-6, 6,1001); %Loop for creating the function zz-1.2*X; figure(1) %Plotting the function hold on plot (X,zz, 'linewidth',3) xlabel(x) ylabel('f(x) title( Plotting of Actual data and Fourier sum) %fourier series Xx-linspace(-18,18,1001) a0-0 an- (n) 0 bn-e (n) ((-0.4*36)/(n+pǐ ) )*cos (n*pi); s-a0/2; for nn-1:20 s-stan ( nn).*cos (nn .#xx. *pi/6)+bn ( nn) . * sin(nn.tXX. *pi/6) ; plot (XX, s, 'linewidth',2) elseif nn--20 plot (XX, s, 'linewidth', 2) end end legend'Actual data', 'Fourier sum for 5 terms, 'Fourier sum for 20 terms') grid on

Plotting of Actual data and Fourier summ 10 Actual data Fourier sum for 5 terms Fourier sum for 20 terms -4 -6 10 20 15 10 10 15 20 Published with MATLAB R2018a

%Matlab code for Fourier Series
clear all
close all
%All time values
X=linspace(-6,6,1001);
%Loop for creating the function
zz=1.2*X;
figure(1)
%Plotting the function
hold on
plot(X,zz,'linewidth',3)
xlabel('x')
ylabel('f(x)')
title('Plotting of Actual data and Fourier sum')

%fourier series
XX=linspace(-18,18,1001);
a0=0;

an=@(n) 0;
bn=@(n) ((-0.4*36)/(n*pi))*cos(n*pi);

s=a0/2;
for nn=1:20
    s=s+an(nn).*cos(nn.*XX.*pi/6)+bn(nn).*sin(nn.*XX.*pi/6);
    if nn==5
        plot(XX,s,'linewidth',2)
    elseif nn==20
        plot(XX,s,'linewidth',2)
    end
end

legend('Actual data','Fourier sum for 5 terms','Fourier sum for 20 terms')
grid on
%%%%%%%%%%%%%% End of Code %%%%%%%%%%%