Question about the Dirac Delta Function

[xoxomae]

Homework Statement

Find the Fourier spectrum of the following equation

Homework Equations

$F(\omega)=\pi[\delta(\omega - \omega _0)+\delta(\omega +\omega_0)]$

The Attempt at a Solution

Would the Fourier spectrum just be two spikes at $+\omega _0$ and $-\omega _0$ which go up to infinity?

 

[BvU]

Yes. My guess is you are supposed to find the function that has such a Fourier transform ?
When you carry out the integration to find that functionl the $\delta$ functions will behave decently -- check the definition of a delta function

 

[George Jones]

xoxmae already has a function $F\left( \omega\right)$ that has two "spikes", one at $\omega = \omega_0$ and one at $\omega = -\omega_0$. The Fourier transform of this will not have spikes.

 

[rude man]

xoxmae already has a function $F\left( \omega\right)$ that has two "spikes", one at $\omega = \omega_0$ and one at $\omega = -\omega_0$. The Fourier transform of this will not have spikes.

He didn't ask for the Fourier transform of F(ω). He asked for the spectrum, i.e. a graph in the frequency domain, which is what BvU said, except it's not sufficient to say " ... spikes which go up to to infinity ..." of course. What of the ω coefficient?

I also agree with BvU that the problem was more likely to find the inverse transform of F(ω).