0
$\begingroup$

enter image description here

I already showed b item using the fact that it is $h\left(0\right)=\int \:f\left(t\right)g\left(0-t\right)dt$

I struggle a lot of hours trying to find the trick in item C.

Can anyone help please ?

$\endgroup$
1
  • $\begingroup$ If you know that $\mathcal{G}$ is the Fourier transform of $g$, do you know the inverse Fourier transform of $g$? $\endgroup$
    – TimWescott
    Jan 12, 2021 at 19:48

1 Answer 1

1
$\begingroup$

Hint:

You only need to use the definition of the Fourier transform and its inverse transform to show that if

$$G(f)=\mathscr{F}\{g(t)\}$$

then

$$g(f)=\mathscr{F}\{G(-t)\}$$

holds. Then just use the result from $b$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.