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

7 views (last 30 days)
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;
fs = zeros(1,n+1);
fs(1,1) = a0;
for i = 2:n+1
fs(1,i) = an(1,i)*sin(i*x);

Accepted Answer

Torsten on 6 Oct 2022
Edited: Torsten on 6 Oct 2022
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);
f = a0 + sum(an.*cos((1:n).*x),2);

More Answers (1)

Walter Roberson
Walter Roberson on 6 Oct 2022
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;
Niloufar on 6 Oct 2022
I wanted to calculate the coefficient of the fourier series but this code gives the wrong 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

Sign in to comment.


Find more on Fourier Analysis and Filtering in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by