Parseval's Theorem

When we consider the inner product of a signal with itself, we have a special case known as Parseval's Theorem:

$$\Vert x \Vert^2 = \left<x,x\right> = \frac{1}{N} \left<X,X\right> = \frac{\Vert X \Vert^2}{N}$$

(Also called the Rayleigh's Energy Theorem.)