Tagged Questions

1
vote
1answer
67 views

What is the odd fourier extention of sin x cos(2x)

odd half range extension of f(x) = sin x cos(2x) with limits 0 to pi
1
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5answers
174 views

Fourier Analysis

I am interested in Fourier Analysis. But I don't get why the coefficients are choosen that way and why the Fourier series will converge to a given function? Can someone provide me simple information ...
1
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0answers
52 views

Proving that two representations of a Fourier series are the same

I have to show that $$\sum_{n=0}^\infty A_n\cos\left({xn\frac{2\pi}{T}-\theta_n}\right) \equiv \sum_{n=-\infty}^\infty c_n \mathrm{e}^{\left({ixn\frac{2\pi}{T}}\right)}$$ I have tried two ...
1
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1answer
164 views

Real part of an integral with complex argument

This is a paper about Fourier cosine series approximation to option pricing problem. The coefficient $A_k$ is defined as $$A_k=\frac{2}{b-a}\int_a^bf(x)\cos\left(k\pi\frac{x-a}{b-a}\right)dx$$ Then ...
5
votes
1answer
161 views

For a polygon on complex plane, when are the vertex 'Fourier coefficients' non-zero

Consider an $n$-sided convex polygon $P$ that contains the origin in the complex plane. Let the $j$-th vertex be denoted $z_j = r_j e^{i\theta_j}$ ($0 \leq \theta_j < 2 \pi$) for $j= 1 \dots n$. ...
4
votes
2answers
413 views

Using complex exponentials as solution of ODE

I'm having trouble wrapping my head around the following issue. My book solves a problem without using complex exponential solution like $C_1 e^{it}$ and using either $A \cos(t) + B \sin(t)$ or $A ...