Parseval equality
\(x(t)\) \(\rightarrow\) \(X(\omega)\)
\(E=\sum_{n=-\infty}^{\infty}\left|x(n)\right|^2=\frac{1}{2\pi}\int_{-\pi}^{\pi}\left|X(\omega)\right|^2d\omega\) (11)
\(E=\frac{1}{2\pi}\int_{-\pi}^{\pi}\left|X(\omega)\right|^2d\omega=\frac{1}{2}\int_{-\pi}^{\pi}{S(}\omega)d\omega\) (12)
\(S\left(\omega\right)=\frac{\left|X(\omega)\right|^2}{2}\) (13)
The signal \(S\left(\omega\right)\) represents the spectral energy density of the signal \(x(n)\).
\(S(\omega+2\pi)=\ S(\omega)\) therefore, the spectral energy density is also periodic with a period of\( 2\pi\).