Fourier Transforms: F[Rect] and F[sinc] Relationship Explanation

[spaghetti3451]

Homework Statement

Explain how F[Rect] = sinc implies F[sinc] = REct +/- a few constants.

Homework Equations

$$2\pi f(-w) = \int^{\infty}_{-\infty} F(t) e^{-iwt} dt$$

The Attempt at a Solution

I have no idea!

 

[vela]

What's the formula for the inverse transform?

 

[spaghetti3451]

of which function exactly?

 

[Redbelly98]

Of any function. What is the defining equation for getting the inverse transform?

 

[ckutlu]

I assume rect is short for "rectangle". The question asks you either to prove duality property of continuous Fourier transform or to use it. Search for the duality, you'll see what i mean.