Question

Hi I was working on calc homework and am currently stuck on a Fourier transform problem. I may be missing something or it could be the wording. Any help would be appreciated. The problem is attached in the link below.

Thank you.

Answer 1

I think you can estimate this using
\[ f \lambda = c \\ \frac{1}{\Delta t}\cdot \Delta x = c \\ \Delta t = \frac{\Delta x}{c} \]
for 1 cm you get about 33 picoseconds.

The Fourier transform of a gaussian is a gaussian, but in the other domain.

Answer 2

I believe we must use an integral. I thank you for your answer but I doubt that this is a simple plug and chug problem.

Answer 3

I know Fourier series but I have no idea about pulses with shapes..
Is there any relation with the Heisenberg uncertainty principle?

Answer 4

Like, both the function and its transform will be bell curves, and you have something like FREQUENCY_thing x TIME_thing \(\ge \frac1{16\pi^2}\).
And you want FREQUENCY_thing to be small ... so that impacts on TIME_thing.