Fourier coefficients of a function
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Paul
2022-5-6
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(...)
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.
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Torsten
2022-5-6
编辑:Torsten
2022-5-6
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))
2 个评论
Torsten
2022-5-6
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))
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