Question

What is the Fourier transform of e^ax? (a>0)

(a) \(\frac{p}{a^2+p^2} \)

(b) \(2 \frac{a}{a^2+p^2} \)

(c) \(-2 \frac{a}{a^2+p^2} \)

(d) cant’t be found

This question was addressed to me during an interview.

The origin of the question is Fourier Transform and Convolution in section Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

The correct option is (d) cant’t be found

The explanation is: Fourier transform of e^ax, does not exist because the function does not converge. The function is divergent.