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It's a very basic question, but I havn't found the question on google or dsp.stackexchange.com: How does integraion of a signal change the spectrum?

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up vote 4 down vote accepted

It is the basic property of Fourier Transforms. Given that $g(t)$ and $G(f)$ are Fourier transform pairs i.e.
$g(t) \rightleftharpoons G(f)$
then
$\int_{-\infty}^tg(\tau)d\tau \rightleftharpoons \frac{1}{j2\pi f}G(f)$

This assumes that $G(0)=0$. If $G(0)$ is not zeros then the integral of $g(t)$ has a Fourier transform that includes a Dirac delta function.

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