how can I plot the fourier series of this function by calculating the coeffcients and for different n?

I don't want to use loop in my code because the speed is low.this is my code but it doesn't work:

x = linspace(-2*pi, 2*pi, 1000);
a0 = 1/2;
n = 5;
an = zeros(1,n);
for i = 1:n
    if mod(4,i)==1
        an(1,i) = 2/i*pi;
    elseif mod(4,i)==3
        an(1,i) = -2/i*pi;
    end
end
fs = zeros(1,n+1);
fs(1,1) = a0;
for i = 2:n+1
    fs(1,i) = an(1,i)*sin(i*x);

end

plot(x,fs,'color','r');

Answer 1

[Torsten]

Note that the function f you defined is even - thus it must be cos(n*x), not sin(n*x) that appears in the Fourier series.

x = linspace(-2*pi, 2*pi, 1000).';
a0 = 1/2;
n = 1000;
an = zeros(1,n);
for i = 1:n
    if mod(i,4)==1
        an(i) = 2/(i*pi);
    elseif mod(i,4)==3
        an(1,i) = -2/(i*pi);
    end
end
f = a0 + sum(an.*cos((1:n).*x),2);
plot(x,f)

[Niloufar]

thank you for your help

Answer 2

[Walter Roberson]

an = zeros(1,n);

i = 1 : n;
mask = mod(4,i) == 3;
an(1,mask) = -2./i(mask) * pi;
mask = mod(4,i) == 1;
an(1,mask) = +2./i(mask) * pi;

[Walter Roberson]

However:

n = 8;
i = 1 : n;
mod(4, i)

ans = 1×8

0 0 1 0 4 4 4 4

That is, the remainder when dividing 4 by 1 is 0, the remainder when dividing 4 by 2 is 0, the remainder when dividing 4 by 3 is 1, the remainder when dividing 4 by 4 is 0, the remainder when dividing 4 by 5 through 8 is 4...

Are you sure that is what you want to do?

[Niloufar]

I wanted to calculate the coefficient of the fourier series but this code gives the wrong answer.an should be zero when n is even and for n=4k+1 should be 2/(n*pi) and for n=4k+3 should be -2/(n*pi) and after that I want to plot the fourier series until desired n. I mean use this formula for calculating the fourier series