The Exact Definition of the Spectral Energy of a Discrete Signal {x[n]}

[Poopsilon]

Is the spectral energy density:

(1) Just the sum of the magnitude of the points at which you've taken the fourier transform, i.e ∑ |X|.

(2) The sum of the absolute value squared of each of these points, i.e ∑ |X|^2.

(3) Or is it the absolute value squared of the sum, i.e | ∑ X |^2.

My professor said it was (2) in class, then in an email he said it was (1), and now I'm looking at the wikipedia article on Spectral Energy Density which is making me think it's (3).

 

[himadrisaha]

This is the Matlab code for theoritical power spectral density.
% theoretical Power spectral density
fc=0;
z1=-10:0.01:10;
d=((z1-fc)/fd).^2;
Sez=(1/(4*pi*fd))*(1./sqrt(1-d));

I think the second one is the right answer cause you need the absolute value square to get the PSD.This is not the absolute value squared of the sum.Then you will not get the exaect value for each point.