How to find out the power (not energy) from the spectrum using Parseval's theorem?

[SherlockBenedict]

How to prove the parseval's theorem for a periodic wave say a sinusiod

Let

x(t)= cos ω_ot

We all know that the fourier transform has two impulses one at ω_o and one at -ω_o and the amplitude of both will be Π (pi)


But you can't prove the Parseval's theorem as the energy will be infinity and both left hand side and right hand side go to infinity.

Well what I would like to know is the power as it is finite for a periodic waveform. Will it be possible to find out the power for the above waveform using Parseval's theorem ( I need to find out the power from the spectrum i.e. frequency domain and prove that power is also conserved in both time and frequency domain) ?


Thanks in advance.

 

[Shug]

I am not sure what you are asking here. Power is something you measure across frequency, or across time; energy of the signal is across frequency/time. As far as the cos function goes, if you integrate a dirac delta function, the integral is one, not infinity.