Show from Equations $-$

$x[k]=\{\begin{array}{cc}{\displaystyle \underset{n=0}{\overset{N-1}{}}}x[n]W_N^{kn},& 0kN-1\end{array}$

$0,$ otherwise

$x[n]=\{\begin{array}{cc}\frac{1}{N}{\displaystyle \underset{k=0}{\overset{N-1}{}}}x[k]W_N^{-kn},& 0nN-1\end{array}$

$0,$ otherwise

that with $x[n]$ as an N $-$point sequence and $x[k]$ as its N $-$point DFT $,$

${\displaystyle \underset{n=0}{\overset{N-1}{}}}|x[n]{|}^2=\frac{1}{N}{\displaystyle \underset{k=0}{\overset{N-1}{}}}|x[k]{|}^2$

This equation is commonly referred to as Parseval's relation for the DFT$>$