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I know final result of Fourier transform of $\cos w_0t$ (from table), but how it is calculated, step by step? Thanks in advance.

hari
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  • Hi and welcome to Math.SE. It is here mandatory to show some effort, to get better help. What are your own thoughts? – mickep Oct 18 '15 at 20:34
  • Fourier transform in $L^2\left(-\frac{\pi}{w_0},\frac{\pi}{w_0}\right)$ ? –  Oct 18 '15 at 20:36

1 Answers1

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My deinition of Fourier transform of $f(t)$ is \begin{equation*} \mathcal{F}[f](x) = \frac{1}{\sqrt{2\pi}} \int_{\mathbb{R}} f(t) e^{-itx} dt \end{equation*} Now just simply compute the integral, and use that the Dirac delta function is also given by \begin{equation*} \delta(x) = \frac{1}{2 \pi} \int_{\mathbb{R}} e^{itx} dt \end{equation*}

Klaramun
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