Question

What is the fourier sine transform of e^-ax?

(a) \(\frac{4}{(4+p^2)} \)

(b) \(4 \frac{a}{(4a^2+p^2 )} \)

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

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

I have been asked this question at a job interview.

This intriguing question originated from Fourier Transform and Convolution in section Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

The correct answer is (c) \(\frac{p}{(a^2+p^2)} \)

The explanation is: Fourier sine transform of \(F(x) = \int_0^∞ e^{-ax}  sin(px)dx \)

\( = \frac{e^{-ax}}{(a^2+p^2 )} (-asin(px)-pcos(px)) \) from 0 to ∞

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