How to create a Fourier series using for loops

Question

Ross King 2022-10-2

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1816020-how-to-create-a-fourier-series-using-for-loops

评论： Torsten 2022-10-2

I am supposed to plot this function on matlab along with another function. I have tried using for loops to create this, I am new to matlab and I don't know what I am doing wrong. Could someone point me in the right direction please? the range for x is from -2 to 2 and NUM is 14

f_init = repelem(0.5,401)
f_approx = (2/((k^2)*(pi^k)))*((-1^k)-1)*cos(k*((pi*x)/2))+(2/(pi*k))*(-1^(k+1))*sin(k*(pi*x/2));
t= length(x)
for k=1:14
    for x=-2:0.01:2
        F(x) = f_init(t)+ f_approx(k);
    end
end
plot(F);

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Answer 1

Torsten 2022-10-2

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1816020-how-to-create-a-fourier-series-using-for-loops#answer_1065065

编辑：Torsten 2022-10-2

在 MATLAB Online 中打开

k = 1:14;

x = (-2:0.01:2).';

f = 0.5 + sum(2./(k.^2*pi^2).*((-1).^k-1).*cos(pi*k.*x/2) + 2./(k*pi).*(-1).^(k+1).*sin(pi*k.*x/2),2);

plot(x,f)

f is a (401x14) matrix with row i made up of the k terms of the Fourier series, evaluated at x(i).

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Ross King 2022-10-2

what does the " . ' " part do? So there are k rows in the f matrix and you add all the terms in the x(ith) column together? What does the dot after the k do in the sum part of your function? I am confused about the why you've put periods in your function.

Torsten 2022-10-2

在 MATLAB Online 中打开

.^, ./ and .* are elementwise operations for vectors and matrices being potentiated, divided or multiplied.

This is in contrast to matrix operations.

Look what comes out if you try

a = [1 2 3];
b = [4 5 6];
a.^b
ans = 1×3
     1    32   729
a./b
ans = 1×3
    0.2500    0.4000    0.5000
a.*b
ans = 1×3
     4    10    18

or

(a.').^b
ans = 3×3
     1     1     1
    16    32    64
    81   243   729
(a.')./b
ans = 3×3
    0.2500    0.2000    0.1667
    0.5000    0.4000    0.3333
    0.7500    0.6000    0.5000
(a.').*b
ans = 3×3
     4     5     6
     8    10    12
    12    15    18