Fourier Series for odd integers only

Question

Tashanda Rayne 2023-12-16

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2061307-fourier-series-for-odd-integers-only

评论： Paul 2023-12-18

Can someone please help me to get this function B to only apply to odd integers but for every other odd integers the formula is negative. So for integer 1,5,9... its positive and for 3,7,11.... its negative

% Fourier Series

syms x k L

f1(x) = x;

f2(x) = L-x;

f1 = simplify(f1);

f2 = simplify(f2);

%Solving for Bn

b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);

b(k) =

b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);

b1(k) =

B(k) = b1 + b

B(k) =

B = simplify(B)

2 个评论
显示无隐藏无

Image Analyst 2023-12-16

I formatted your code as code so people can easily copy it into their MATLAB, and I ran the code. But I'm not sure what you're asking. What are the "integers" that you're talking about?

Paul 2023-12-18

I see that one issue in the code has been fixed, but I still think the equations for b(k) and b1(k) are incorrect based on my assumption of what the goal of this code actually is.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Walter Roberson 2023-12-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2061307-fourier-series-for-odd-integers-only#answer_1372847

在 MATLAB Online 中打开

symsum( (-1)^(k+1)*B(2*k-1), k, 1, inf)

2 个评论
显示无隐藏无

Walter Roberson 2023-12-16

在 MATLAB Online 中打开

% Fourier Series

syms x k L

f1(x) = x;

f2(x) = L-x;

f1 = simplify(f1);

f2 = simplify(f2);

%Solving for Bn

b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);

b(k) = simplify(b(k))

b(k) =

b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);

b1(k) = simplify(b(k))

b1(k) =

B(k) = b1 + b

B(k) =

syms N integer

val(N) = symsum( (-1)^(k+1)*B(2*k-1), k, 1, N)

val(N) =

val(25)

ans =

vpa(ans)

ans =

val(100)

ans =

vpa(ans)

ans =

val(200)

ans =

vpa(ans)

ans =

val(1234)

ans =

vpa(ans)

ans =

val(inf)

ans =

NaN

Walter Roberson 2023-12-18

在 MATLAB Online 中打开

% Fourier Series

syms x k L

f1(x) = x;

f2(x) = L-x;

f1 = simplify(f1);

f2 = simplify(f2);

%Solving for Bn

b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);

b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);

B(k) = b1 + b

B(k) =

B = simplify(B)

B(k) =

syms N integer

val(N) = symsum( (-1)^(k+1)*B(2*k-1), k, 1, N)

val(N) =

val(100), vpa(ans)

ans =

val(200), vpa(ans)

ans =

val(201), vpa(ans)

ans =

请先登录，再进行评论。

Answer 2

Paul 2023-12-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2061307-fourier-series-for-odd-integers-only#answer_1372882

在 MATLAB Online 中打开

Hi Tashanda,

I see a couple of issues with the code

Though not an error, it would be clearer if you specified the variable of integration. And it's always best to use sym(pi). With these changes, the equation for b(k) would look like

%b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);
b(k)  = (2/L)*int(f1*sin(k*sym(pi)*x/L),x,[0,L/2]);
b(k)  = simplify(b(k))

But even with those changes, the equation for b(k) is incorrect. Go back to your source and carefully compare this code to what the equation should be.

Then, the same comments apply to b1(k).

b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);

Finally, this line is a typo. i don't think you want b(k) on the right hand side.

b1(k) = simplify(b(k))