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I have question for which i am stuck at

Calculate the Fourier Transform of $f(x) = e^-((x-1)^2)/4$

I am not sure if my answer is correct since it makes no sense...

Orenio
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Nap Queen
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  • Hi and welcome to MSE. Please use mathjax to format the question. Also show us your efforts on the problem to avoid this question being highly downvoted or being closed. See this link to know how to ask a good question on this website – sai-kartik May 05 '20 at 17:10

1 Answers1

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$$ f(x) = e^{\left(-\frac{1}{4} \, {\left(x - 1\right)}^{2}\right)} $$ applying the definition of the fourier transform yields $$ \mathfrak{F} (\xi) = \int_{-\infty}^{\infty} e^{-2 \, \pi x \xi - \frac{1}{4} \, {\left(x - 1\right)}^{2}} dx $$ $$ = 2 \, \sqrt{\pi} e^{\left(4 \, \pi^{2} \xi^{2} - 2 \, \pi \xi\right)} $$

Alexandru Ionut
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