(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the Fourier Transform of:

f(t)=[itex]\frac{cos(\alpha t)}{t^2+\beta^2}[/itex]

2. Relevant equations

F[itex](\omega)[/itex]=[itex]\frac{1}{2\pi}[/itex][itex]\int[/itex][itex]^{∞}_{-∞}[/itex][itex]\frac{cos(\alpha t)exp(i \omega t)}{t^2+\beta^2}[/itex]

3. The attempt at a solution

I start with:

[itex]cos(\alpha t)[/itex]=[itex]\frac{exp(i \alpha t)+exp(-i \alpha t)}{2}[/itex]

Substituting this in, I get:

[itex]F(\omega)[/itex]=[itex]\frac{1}{4\pi}\int^{∞}_{-∞}\frac{exp(it(\alpha+\omega))+exp(it(\omega-\alpha))}{t^2+\beta^2}[/itex]

From here I know I should be able to get this in the form of some delta functions but I can't figure out the manipulation. I'd appreciate any help!

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# Homework Help: Help finding Fourier Transform!

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