How to plot correctly a Fourier series?

Question

Szalka Gergo 2021-5-11

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/827640-how-to-plot-correctly-a-fourier-series

编辑： Aghamarsh Varanasi 2021-5-26

在 MATLAB Online 中打开

Hi,

I would like to solve this problem related with Fourier series:

I have successfully determined a0, an, and bn. Now I would like to compute first 5,10,15 terms with MATLAB.

My (semi-finished) code:

clear;
max = 5;  % first 5 terms
syms t
y = piecewise(-3<t<0,-6,0<t<3,-2);
I = [-3,3];
fplot(y, I)  % plot original func.
hold on;
syms x n;
fun1 = -6;
fun2 = -2;
fun3 = fun1 * cos((n * pi) / 3 * x);
fun4 = fun2 * cos((n * pi) / 3 * x);
fun5 = fun1 * sin((n * pi) / 3 * x);
fun6 = fun2 * sin((n * pi) / 3 * x);
a0 = (1/3) * int(fun1,x,[-3 0]) + (1/3) * int(fun2,x,[0 3]);
an = (1/3) * int(fun3,x,[-3 0]) + (1/3) * int(fun4,x,[0 3]);
bn = (1/3) * int(fun5,x,[-3 0]) + (1/3) * int(fun6,x,[0 3]);
c = 0;
AN = [];
for i = 1:max
    c= c+1;
    AN = [AN subs(an,n,c)];
    i = i+1;
end
c = 0;
BN = [];
for i = 1:max
    c= c+1;
    BN = [BN subs(bn,n,c)];
    i = i+1;
end

an and bn values are stored in AN and BN vectors. It seems that this code compute terms correctly, but I don't know how to plot this function.

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Answer 1

Aghamarsh Varanasi 2021-5-26

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/827640-how-to-plot-correctly-a-fourier-series#answer_709260

编辑：Aghamarsh Varanasi 2021-5-26

在 MATLAB Online 中打开

Hi,

You can create a 'fourier series' with the coefficients a0, AN and BN arrays and use fplot to plot this symbolic function.

For example, the last part of your code can be modified as follows

AN = [];
BN = [];
fourier_series = 0;
for i = 1:max
    AN = [AN subs(an,n,i)];
    BN = [BN subs(bn,n,i)];
    
    fourier_series = fourier_series + (AN(i) *  cos(i*t) + BN(i) * sin(i*t));
end
fplot(t, (a0/2 + fourier_series), [-3,3])