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| un:power-spectrum [2023/05/05 04:42] – asad | un:power-spectrum [2023/05/05 04:50] (current) – asad | ||
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| ====== Power spectrum ====== | ====== Power spectrum ====== | ||
| - | Power spectrum, a two-point correlation function, | + | Power spectrum is a powerful tool for analyzing structures in the universe from the very smallest to the very largest. It is nothing but the square of the amplitude of the [[Fourier transform]] of a dataset, mathematically |
| $$ P(k) = |F(k)|^2 $$ | $$ P(k) = |F(k)|^2 $$ | ||
| where $F(k)$ is the Fourier transform of a function $f(\theta)$ and $k\sim \theta^{-1}$ is the Fourier scale or frequency corresponding to the variable $\theta$. A power spectrum gives the power $P(k)$ at different scales $k$. | where $F(k)$ is the Fourier transform of a function $f(\theta)$ and $k\sim \theta^{-1}$ is the Fourier scale or frequency corresponding to the variable $\theta$. A power spectrum gives the power $P(k)$ at different scales $k$. | ||
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| + | ====== Surface ====== | ||
| + | |||
| + | ====== Cube ====== | ||
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un/power-spectrum.1683283352.txt.gz · Last modified: 2023/05/05 04:42 by asad