怎样用MATLAB操作求函数f(x)=²在[-π,π]上的傅里叶级数。

Answer 1

The general explain of Fourier series is in the follwoing link:

https://zh.wikipedia.org/wiki/%E5%82%85%E9%87%8C%E5%8F%B6%E7%BA%A7%E6%95%B0

I am not sure your question is, since f(x) = [empty]^2 !?

So I assumed that your question is related to x^2 in the domain of [-pi, pi], the re-written question is shown below.

The code is:

clear all
figure

for nmax   = 2:2:20
    
    x    = -2:.01:2;
    a0   = pi^2/3;
    fn = a0;
    plot(x,x.^2,'linewidth',2,'color',[0 0 0]+.8)
    axis([-3 3 0 4]), grid on, hold on

    for n  = 1:1:nmax
        an = (-1)^n*4/n^2*cos(n*x);
        fn = fn + an;
    end
    plot(x,fn,'linewidth',2,'color','k')
    axis([-3 3 0 4]), grid on, pause(1)
    
    hold off
    
end

The output of this code is