# Question about the Dirac Delta Function

1. Apr 14, 2016

### xoxomae

1. The problem statement, all variables and given/known data
Find the Fourier spectrum of the following equation

2. Relevant equations
$F(\omega)=\pi[\delta(\omega - \omega _0)+\delta(\omega +\omega_0)]$

3. The attempt at a solution
Would the Fourier spectrum just be two spikes at $+\omega _0$ and $-\omega _0$ which go up to infinity?

2. Apr 14, 2016

### 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

3. Apr 14, 2016

### George Jones

Staff Emeritus
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.

4. Apr 22, 2016

### rude man

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).