Fourier coefficients of a function

given this function with this interval is there any way to calculate the Fourier coefficients (ak, a0, bk) of this fuction in matlab?

Answer 1

[Paul]

Hi SSBGH

If you want a closed form solution, use the symbolic toolbox to define f(x)

syms x
f(x) = ....

Once you have that you can use the symbolic toolbox to compute a0, ak, and bk in terms of their defining integrals using the int function

syms k integer positive
a0 = int(...)
ak = int(...)
bk = int(...)

The defining integrals should be in your notes or text book, or can be found here.

If you want to numerically compute a0, ak, and bk for given values of k, first define f(x) as an anonymous function

f = @(x) ....

Then use the integral function to compute a0, or ak, or bk for a specific value of k

Your're more likely to get more help if you post your code and explain where you think it might be having problems.

[SSBGH]

thanks alot man

Answer 2

[Torsten]

syms x omega n
f = 0.5*(sin(x)+abs(sin(x)));
F(omega) = int(f*exp(1i*omega*x),x,-pi,pi)
n = 10;
g = real(F(0))/(2*pi) + sum(real(F(1:n))/pi.*cos((1:n)*x)+imag(F(1:n))/pi.*sin((1:n)*x))
g = matlabFunction(g);
x = linspace(-pi,pi,100)
plot(x,g(x))
hold on
f = matlabFunction(f);
plot(x,f(x))

[SSBGH]

after writing your code im getting bunch of errors do you know why?

[Torsten]

I don't know. Maybe MATLAB cannot evaluate F(1).

Try

g = real(F(0))/(2*pi) + 0.5*sin(x) + sum(real(F(2:n))/pi.*cos((2:n)*x)+imag(F(2:n))/pi.*sin((2:n)*x))