In lectures, I have learnt that [tex]F(k)= \int_{-\infty}^{\infty} e^{-ikx}f(x)dx[/tex] where F(k) is the fourier transform of f(x) and the inverse fourier transform is [tex]f(x)= \frac{1}{2\pi}\int_{-\infty}^{\infty} e^{ikx}f(k)dk[/tex] .(adsbygoogle = window.adsbygoogle || []).push({});

But on the same chapter in the lecture notes, there is an example solving for the fourier transform of [itex]f(x)=(\delta(x+d))+(\delta(x-d))[/itex].

I set the transform as [tex]F(k)= \int_{-\infty}^{\infty} e^{-ikx}(\delta(x+d))+(\delta(x-d))dx[/tex]Splitting the integral into two and using the sifting property, I got [tex]F(k)=e^{ikd}+e^{-ikd}[/tex] But the solution has [itex]\frac{1}{\sqrt{2\pi}}[/itex] in front, hence from there they used the trig identity to get it in terms of cosine.

I searched on google and there seems to be different conventions on the transform. But I am only familiar with the one I mentioned. How can I get to the solution using the integral form I used?

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# I Fourier transform of Dirac delta

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