- #1

Telemachus

- 835

- 30

Hi there. I have some trouble with this. I have to find the inverse Fourier transform for: [tex]\frac{e^{i 6\omega}}{\omega}[/tex]

So I'm using a table, then:

[tex]F^{-1}\left ( \frac{e^{i 6\omega}}{\omega}\right )=F^{-1}\left ( e^{i 6\omega}\right ) * F^{-1}\left ( \frac{1}{\omega}\right )=2\pi\left[ \delta (t+6)*\frac{i}{2}sg(t)\right][/tex] where (*) represents the convolution.

Well, everything fine till there, but when I tried to corroborate my result with mathematica I get:

I don't know what's wrong.

So I'm using a table, then:

[tex]F^{-1}\left ( \frac{e^{i 6\omega}}{\omega}\right )=F^{-1}\left ( e^{i 6\omega}\right ) * F^{-1}\left ( \frac{1}{\omega}\right )=2\pi\left[ \delta (t+6)*\frac{i}{2}sg(t)\right][/tex] where (*) represents the convolution.

Well, everything fine till there, but when I tried to corroborate my result with mathematica I get:

I don't know what's wrong.