about Parseval's theorem 1

[lxu]

Hello

Can anyone help me with this? I have a question regarding Parseval's theorem. Consider the case of Dirac delta funtion. It's Fourier transform is a constant in frequency domain, right? However, the delta function has finite energy, but the integral of constant over the whole frequency domain will give an infinite value. does this agree with the Parseval's theorem?

thanks,
Xu

 

[VisiGoth]

If the constant in the frequency domain is zero, the energy would not be infinite. As the dirac function approaches zero width in the time doamin it also apporaches zero height in the freuqncy doamain.

There is also an out. The Parseval theorem requires the function to bounded and tegrable (and I think it needs to be square integrable also). Your Dirac is not bounded therefore Parseval does not have to work. We can see that we can apprach the correct eqality limit as the amplitude tends toward unbounded, which might give you some comfort.

 

[Skogsgurra]

Thanks VisiGoth! This is something I have been wondering about, too. We tend to forget about reality when dealing with infinity.

Gunnar Englund

http://www.gke.org