Fourier series plot as sums of sines and cosines

Hi there,

founding troubles in plotting a simple Fourier series.

f(x)=16pi^4\5+16Σ((2pi^2\n^2)-(3\n^4))cos(nx)+16piΣ(3\n^3)-(pi^2\4n))sin(nx)

from 0 to 5

then from 0 to 10 and then compare with the real cosx function,

I know, I am J.... but I cannot figure it out. I tried with the examples posted but nothing seems to be working.

Can any good samaritan help me figuring this out? Thank U all!

[Antonello Carloni]

This is the printed version

Answer 1

[Sulaymon Eshkabilov]

This can be done in a few different ways, such as vectorization, [for .. end] and [while .. end] loops. E.g.:

clc; clearvars; close all;
x = linspace(0, 2*pi, 500);
S = 16*pi*4/5;
n = 1:5;
S1 = 16*((2*pi^2./n(:).^2)-(3/n(:).^4))*cos(n(:).*x);
S2 = 16*pi*((3./n(:).^3)-((pi^2)./n(:).^3)).*sin(n(:).*x);
SS_n5 = S+sum(S1)+sum(S2);
subplot(211)
plot(x, SS_n5, 'r-'); title('n = 1:5')
n = 1:10;
S1 = 16*((2*pi^2./n(:).^2)-(3/n(:).^4))*cos(n(:).*x);
S2 = 16*pi*((3./n(:).^3)-((pi^2)./n(:).^3)).*sin(n(:).*x);
SS_n10 = S+sum(S1)+sum(S2);
subplot(212)
plot(x, SS_n10, 'b-')
title('n = 1:10')

figure()
plot(x, SS_n5, 'r', 'DisplayName', 'n=1:5'), hold on
plot(x, SS_n10, 'b', 'DisplayName', 'n=1:10')
legend, grid on; shg
title('Fourier Series')

[Antonello Carloni]

Thank you! 7 blessings!

[Sulaymon Eshkabilov]

Most welcome!