Fourier series doesn't approximate with bigger number of points

Question

reddlno 2022-3-14

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1671484-fourier-series-doesn-t-approximate-with-bigger-number-of-points

评论： Torsten 2022-3-15

Hello.

I am trying to approximate a function using fourier series, but using a larger input of points N I get an aproximation bigger than the original graph. I can't seem to find where the problem is any help is appreciated. First plot is the function, then it's the fourier series versus precise graph and then An and Bn koeficient correlation from N.

code:

clc
clear
%conditions
T=3;
h=0.1;
a=-3;
b=3;
N=36;
x=a:h:b;
n1=0;
%original function
for iks=a:h:b
    n1=n1+1;
    graf1(1,n1)=iks;
    graf1(2,n1)=funk(iks);
end
%plot
plot(graf1(1,:),graf1(2,:));
ylabel('y')
xlabel('x')
%Fourier series and aproximation
A0=0;
for iks2=0:h:T
    A0=A0+funk(iks2);
end
A0=A0.*2.*h./T;
AnBn=zeros(3,N);
for nr=1:N
    for n2=-T:h:T
        AnBn(1,nr)=AnBn(1,nr)+funk(n2)*cos(2*nr*pi*n2/T);
        AnBn(2,nr)=AnBn(2,nr)+funk(n2)*sin(2*nr*pi*n2/T);
    end
end
AnBn=AnBn.*h./T;
n3=0;
aprox1=zeros(2,(b-a)./h);
for iks3=a:h:b
    aprox=0;
    for k=1:N
        aprox=aprox+(AnBn(1,k).*cos(2*k*pi*iks3/T)+AnBn(2,k).*sin(2*k*pi*iks3/T));
    end
    aprox=aprox+A0/2;
    n3=n3+1;
    aprox1(1,n3)=iks3;
    aprox1(2,n3)=aprox;
end
%ploting
figure
plot(aprox1(1,:),aprox1(2,:),'b',graf1(1,:),graf1(2,:),'r');
ylabel('y')
xlabel('x')
legend('Aproksimated f','Original f')
for nr1=1:N
    AnBn(3,nr1)=nr1;
end
figure
scatter(AnBn(3,:),AnBn(1,:),'r')
ylabel('An')
xlabel('N')
figure
scatter(AnBn(3,:),AnBn(2,:))
ylabel('Bn')
xlabel('N')
funk:
function [y] = funk(x)
T=3;
x1=1.0;
x2=x1+0.5*pi;
if (x<0)
    while (x<0)
        x=x+T;
    end
elseif (x>T)
    while (x>T)
        x=x-T;
    end
end
if (0<=x && x<x1)
    y=0;
elseif (x1<=x && x<=x2)
    y=sin(2*(x-x1)).^2;
    
elseif (x2<x && x<=T)
    y=0;
end
end