What is the DFT of DFT of discrete signal What is the discrete fourier transform of the discrete fourier transform of any discrete time signal. Is result same signal? How?
let

$$\begin{align}
 X[k] &amp;= \mathcal{DFT} \Big\{ x[n] \Big\} \\
      &amp;\triangleq \sum\limits_{n=0}^{N-1} x[n] \, e^{-j2\pi nk/N}
\end{align} $$

and 

$$ y[n] \triangleq X[n]  $$

(note the substitution of $n$ in for $k$.)  then

$$ Y[k] = \mathcal{DFT} \Big\{ y[n] \Big\} $$

then, if the DFT is defined the most common way (as above):

$$ Y[n] = N \cdot x[-n] $$

where periodicity is implied:  $x[n+N]=x[n]$ for all $n$.