- #1
Niles
- 1,866
- 0
Homework Statement
Hi
I wish to Fourier transform the following expression
[tex]
P(t) = \int\limits_{ - \infty }^\infty {dt_1 dt_2 \chi (t - t_1 ,t - t_2 )E(t_1 )E(t_2 )}
[/tex]
What I do is the following
[tex]
\int\limits_{ - \infty }^\infty {P(\omega )e^{ - i\omega t} } = \int\limits_{ - \infty }^\infty {dt_1 dt_2 d\omega _1 d\omega _2 \,\chi (\omega _1 ,\omega _2 )E(\omega _1 )E(\omega _2 )e^{ - i\omega _1 (t - t_1 )} e^{ - i\omega _2 (t - t_2 )} e^{ - i\omega _1 t_1 } e^{ - i\omega _2 t_2 } }
[/tex]
I'm pretty sure I need to keep rewriting the expressions on the LHS and RHS until I reach a point, where I can compare the terms to each other. But do you have a hint for what I need to do from here?
Cheers,
Niles.