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Questions tagged [fast-fourier-transform]

Use this tag for questions related to the fast Fourier transform, an algorithm that samples a signal over a period of time (or space) and divides it into its frequency components.

12
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3answers
4k views

How does FFT work?

For five years I tried to understand how Fourier transform works. Read a lot of articles, but nobody could explain it in simple terms. Two weeks ago I stumbled upon the video about a 100 years old ...
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1answer
973 views

Complexity of FFT algorithms (Cooley-Tukey, Bluestein, Prime-factor)

I need to be able to explain the complexity of three Fast Fourier Transform algorithms: Cooley-Tukey's, Bluestein's and Prime-factor algorithm. Unfortunatelly, I'm a little lost in the process. ...
1
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1answer
2k views

Find the solution of the Dirichlet problem in the half-plane y>0.

Find the solution of the Dirichlet problem in the half-plane $y>0$. $${u_y}_y +{u_x}_x=0, -\infty<x<\infty,y>0$$ $$u(x,0)=f(x),-\infty<x<\infty$$ $u$ and $u_x$ vanish as $$ \lvert ...
2
votes
0answers
103 views

Discrete versions of the Fourier Slice-Projection Theorem

I understand the continuous version of the Fourier Slice-Projection theorem, which says that given a (nice enough) function $f:\mathbb{R}^3\to\mathbb{C}$ the following operations give the same result: ...
1
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1answer
259 views

Convolution of function with singularity

I want to numerically evaluate a convolution that contains the function $$f(t) = \dfrac{1}{e^{t}-1},$$ like $$h(t) = f(t) \circ g(t)$$ where $g(t)$ is a smooth well-behaved function that converges ...